المؤلفون: Li, Yanjiang, Yu, Zhongqing, Huang, Yumei

مصطلحات موضوعية: keyword:chemotaxis, keyword:Navier-Stokes system, keyword:self-consistent, keyword:global existence, keyword:boundedness, msc:35K55, msc:35Q35, msc:35Q92, msc:92C17

وصف الملف: application/pdf

Relation: reference:[1] Bellomo, N., Bellouquid, A., Tao, Y., Winkler, M.: Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues.Math. Models Methods Appl. Sci. 25 (2015), 1663-1763. Zbl 1326.35397, MR 3351175, 10.1142/S021820251550044X; reference:[2] Bellomo, N., Outada, N., Soler, J., Tao, Y., Winkler, M.: Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision.Math. Models Methods Appl. Sci. 32 (2022), 713-792. Zbl 1497.35039, MR 4421216, 10.1142/S0218202522500166; reference:[3] Cao, X.: Global classical solutions in chemotaxis(-Navier)-Stokes system with rotational flux term.J. Differ. Equations 261 (2016), 6883-6914. Zbl 1352.35092, MR 3562314, 10.1016/j.jde.2016.09.007; reference:[4] Carrillo, J. A., Peng, Y., Xiang, Z.: Global existence and decay rates to self-consistent chemotaxis-fluid system.Available at https://arxiv.org/abs/2302.03274 (2023), 36 pages. MR 4671518; reference:[5] Chae, M., Kang, K., Lee, J.: Existence of smooth solutions to coupled chemotaxis-fluid equations.Discrete Contin. Dyn. Syst. 33 (2013), 2271-2297. Zbl 1277.35276, MR 3007686, 10.3934/dcds.2013.33.2271; reference:[6] Chae, M., Kang, K., Lee, J.: Global existence and temporal decay in Keller-Segel models coupled to fluid equations.Commun. Partial Differ. Equations 39 (2014), 1205-1235. Zbl 1304.35481, MR 3208807, 10.1080/03605302.2013.852224; reference:[7] Francesco, M. Di, Lorz, A., Markowich, P. A.: Chemotaxis-fluid coupled model for swimming bacteria with nonlinear diffusion: Global existence and asymptotic behavior.Discrete Contin. Dyn. Syst. 28 (2010), 1437-1453. Zbl 1276.35103, MR 2679718, 10.3934/dcds.2010.28.1437; reference:[8] Duan, R., Li, X., Xiang, Z.: Global existence and large time behavior for a two-dimensional chemotaxis-Navier-Stokes system.J. Differ. Equations 263 (2017), 6284-6316. Zbl 1378.35160, MR 3693175, 10.1016/j.jde.2017.07.015; reference:[9] Duan, R., Lorz, A., Markowich, P. A.: Global solutions to the coupled chemotaxis-fluid equations.Commun. Partial Differ. Equations 35 (2010), 1635-1673. Zbl 1275.35005, MR 2754058, 10.1080/03605302.2010.497199; reference:[10] Galdi, G. P.: An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Vol. I: Linearized Steady Problems.Springer Tracts in Natural Philosophy 38. Springer, Berlin (1994). Zbl 0949.35004, MR 1284205, 10.1007/978-1-4757-3866-7; reference:[11] He, P., Wang, Y., Zhao, L.: A further study on a 3D chemotaxis-Stokes system with tensor-valued sensitivity.Appl. Math. Lett. 90 (2019), 23-29. Zbl 1410.35249, MR 3875493, 10.1016/j.aml.2018.09.019; reference:[12] Horstmann, D.: From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I.Jahresber. Dtsch. Math.-Ver. 105 (2003), 103-165. Zbl 1071.35001, MR 2013508; reference:[13] Ishida, S.: Global existence and boundedness for chemotaxis-Navier-Stokes systems with position-dependent sensitivity in 2D bounded domains.Discrete Contin. Dyn. Syst. 35 (2015), 3463-3482. Zbl 1308.35214, MR 3320134, 10.3934/dcds.2015.35.3463; reference:[14] Jin, C.: Global bounded solution in three-dimensional chemotaxis-Stokes model with arbitrary porous medium slow diffusion.Available at https://arxiv.org/abs/2101.11235 (2021), 24 pages.; reference:[15] Jin, C., Wang, Y., Yin, J.: Global solvability and stability to a nutrient-taxis model with porous medium slow diffusion.Available at https://arxiv.org/abs/1804.03964 (2018), 35 pages. MR 4635735; reference:[16] Keller, E. F., Segel, L. A.: Initiation of slime mold aggregation viewed as an instability.J. Theor. Biol. 26 (1970), 399-415. Zbl 1170.92306, MR 3925816, 10.1016/0022-5193(70)90092-5; reference:[17] Kozono, H., Yanagisawa, T.: Leray's problem on the stationary Navier-Stokes equations with inhomogeneous boundary data.Math. Z. 262 (2009), 27-39. Zbl 1169.35045, MR 2491599, 10.1007/s00209-008-0361-2; reference:[18] Li, X., Wang, Y., Xiang, Z.: Global existence and boundedness in a 2D Keller-Segel-Stokes system with nonlinear diffusion and rotational flux.Commun. Math. Sci. 14 (2016), 1889-1910. Zbl 1351.35073, MR 3549354, 10.4310/CMS.2016.v14.n7.a5; reference:[19] Liu, J.-G., Lorz, A.: A coupled chemotaxis-fluid model: Global existence.Ann. Inst. H. Poincaré, Anal. Non Linéaire 28 (2011), 643-652. Zbl 1236.92013, MR 2838394, 10.1016/J.ANIHPC.2011.04.005; reference:[20] Lorz, A.: Coupled chemotaxis fluid model.Math. Models Methods Appl. Sci. 20 (2010), 987-1004. Zbl 1191.92004, MR 2659745, 10.1142/S0218202510004507; reference:[21] Patlak, C. S.: Random walk with persistence and external bias.Bull. Math. Biophys. 15 (1953), 311-338. Zbl 1296.82044, MR 0081586, 10.1007/BF02476407; reference:[22] Peng, Y., Xiang, Z.: Global existence and boundedness in a 3D Keller-Segel-Stokes system with nonlinear diffusion and rotational flux.Z. Angew. Math. Phys. 68 (2017), Article ID 68, 26 pages. Zbl 1386.35189, MR 3654908, 10.1007/s00033-017-0816-6; reference:[23] Tan, Z., Zhang, X.: Decay estimates of the coupled chemotaxis-fluid equations in $\Bbb{R}^3$.J. Math. Anal. Appl. 410 (2014), 27-38. Zbl 1333.92015, MR 3109817, 10.1016/j.jmaa.2013.08.008; reference:[24] Tao, Y.: Boundedness in a chemotaxis model with oxygen consumption by bacteria.J. Math. Anal. Appl. 381 (2011), 521-529. Zbl 1225.35118, MR 2802089, 10.1016/j.jmaa.2011.02.041; reference:[25] Tao, Y., Winkler, M.: Global existence and boundedness in a Keller-Segel-Stokes model with arbitrary porous medium diffusion.Discrete Contin. Dyn. Syst. 32 (2012), 1901-1914. Zbl 1276.35105, MR 2871341, 10.3934/dcds.2012.32.1901; reference:[26] Tuval, I., Cisneros, L., Dombrowski, C., Wolgemuth, C. W., Kessler, J. O., Goldstein, R. E.: Bacterial swimming and oxygen transport near contact lines.Proc. Natl. Acad. Sci. USA 102 (2005), 2277-2282. Zbl 1277.35332, 10.1073/pnas.0406724102; reference:[27] Wang, Y.: Global solvability in a two-dimensional self-consistent chemotaxis-Navier- Stokes system.Discrete Contin. Dyn. Syst., Ser. S 13 (2020), 329-349. Zbl 1442.35481, MR 4043697, 10.3934/dcdss.2020019; reference:[28] Wang, Y., Winkler, M., Xiang, Z.: Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity.Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 18 (2018), 421-466. Zbl 1395.92024, MR 3801284, 10.2422/2036-2145.201603_004; reference:[29] Wang, Y., Winkler, M., Xiang, Z.: The small-convection limit in a two-dimensional chemotaxis-Navier-Stokes system.Math. Z. 289 (2018), 71-108. Zbl 1397.35322, MR 3803783, 10.1007/s00209-017-1944-6; reference:[30] Wang, Y., Zhao, L.: A 3D self-consistent chemotaxis-fluid system with nonlinear diffusion.J. Differ. Equations 269 (2020), 148-179. Zbl 1436.35238, MR 4081519, 10.1016/j.jde.2019.12.002; reference:[31] Winkler, M.: Absence of collapse in a parabolic chemotaxis system with signal-dependent sensitivity.Math. Nachr. 283 (2010), 1664-1673. Zbl 1205.35037, MR 2759803, 10.1002/mana.200810838; reference:[32] Winkler, M.: Aggregation vs. global diffusive behavior in the higher-dimensional Keller- Segel model.J. Differ. Equations 248 (2010), 2889-2905. Zbl 1190.92004, MR 2644137, 10.1016/j.jde.2010.02.008; reference:[33] Winkler, M.: Global large-data solutions in a chemotaxis-(Navier-)Stokes system modeling cellular swimming in fluid drops.Commun. Partial Differ. Equations 37 (2012), 319-351. Zbl 1236.35192, MR 2876834, 10.1080/03605302.2011.591865; reference:[34] Winkler, M.: Stabilization in a two-dimensional chemotaxis-Navier-Stokes system.Arch. Ration. Mech. Anal. 211 (2014), 455-487. Zbl 1293.35220, MR 3149063, 10.1007/s00205-013-0678-9; reference:[35] Winkler, M.: Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity.Calc. Var. Partial Differ. Equ. 54 (2015), 3789-3828. Zbl 1333.35104, MR 3426095, 10.1007/s00526-015-0922-2; reference:[36] Winkler, M.: Global weak solutions in a three-dimensional chemotaxis-Navier-Stokes system.Ann. Inst. H. Poincaré, Anal. Non Linéaire 33 (2016), 1329-1352. Zbl 1351.35239, MR 3542616, 10.1016/J.ANIHPC.2015.05.002; reference:[37] Winkler, M.: How far do chemotaxis-driven forces influence regularity in the Navier- Stokes system?.Trans. Am. Math. Soc. 369 (2017), 3067-3125. Zbl 1356.35071, MR 3605965, 10.1090/tran/6733; reference:[38] Winkler, M.: Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement.J. Differ. Equations 264 (2018), 6109-6151. Zbl 1395.35038, MR 3770046, 10.1016/j.jde.2018.01.027; reference:[39] Winkler, M.: A three-dimensional Keller-Segel-Navier-Stokes system with logistic source: Global weak solutions and asymptotic stabilization.J. Funct. Anal. 276 (2019), 1339-1401. Zbl 1408.35132, MR 3912779, 10.1016/j.jfa.2018.12.009; reference:[40] Yu, P.: Global existence and boundedness in a chemotaxis-Stokes system with arbitrary porous medium diffusion.Math. Methods Appl. Sci. 43 (2020), 639-657. Zbl 1439.35254, MR 4056454, 10.1002/mma.5920; reference:[41] Zhang, Q., Li, Y.: Convergence rates of solutions for a two-dimensional chemotaxis- Navier-Stokes system.Discrete Contin. Dyn. Syst., Ser. B 20 (2015), 2751-2759. Zbl 1334.35104, MR 3423254, 10.3934/dcdsb.2015.20.2751; reference:[42] Zhang, Q., Li, Y.: Global weak solutions for the three-dimensional chemotaxis-Navier- Stokes system with nonlinear diffusion.J. Differ. Equations 259 (2015), 3730-3754. Zbl 1320.35352, MR 3369260, 10.1016/j.jde.2015.05.012; reference:[43] Zhang, Q., Zheng, X.: Global well-posedness for the two-dimensional incompressible chemotaxis-Navier-Stokes equations.SIAM J. Math. Anal. 46 (2014), 3078-3105. Zbl 1444.35011, MR 3252810, 10.1137/130936920; reference:[44] Zheng, J.: Global existence and boundedness in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity.Ann. Mat. Pura Appl. (4) 201 (2022), 243-288. Zbl 1485.35119, MR 4375009, 10.1007/s10231-021-01115-4

الاتاحة: http://hdl.handle.net/10338.dmlcz/152273

المؤلفون: Zhao, Xiangdong

مصطلحات موضوعية: keyword:chemotaxis, keyword:singular sensitivity, keyword:global solvability, msc:35B45, msc:35K55, msc:92C17

وصف الملف: application/pdf

Relation: reference:[1] Black, T.: Global generalized solutions to a parabolic-elliptic Keller-Segel system with singular sensitivity.Discrete Contin. Dyn. Syst., Ser. S 13 (2020), 119-137. Zbl 1439.35486, MR 4043685, 10.3934/dcdss.2020007; reference:[2] Ding, M., Wang, W., Zhou, S.: Global existence of solutions to a fully parabolic chemotaxis system with singular sensitivity and logistic source.Nonlinear Anal., Real World Appl. 49 (2019), 286-311. Zbl 1437.35118, MR 3936798, 10.1016/j.nonrwa.2019.03.009; reference:[3] Fujie, K.: Boundedness in a fully parabolic chemotaxis system with singular sensitivity.J. Math. Anal. Appl. 424 (2015), 675-684. Zbl 1310.35144, MR 3286587, 10.1016/j.jmaa.2014.11.045; reference:[4] Fujie, K., Senba, T.: Global existence and boundedness in a parabolic-elliptic Keller-Segel system with general sensitivity.Discrete Contin. Dyn. Syst., Ser. B 21 (2016), 81-102. Zbl 1330.35051, MR 3426833, 10.3934/dcdsb.2016.21.81; reference:[5] Fujie, K., Senba, T.: Global existence and boundedness of radial solutions to a two dimensional fully parabolic chemotaxis system with general sensitivity.Nonlinearity 29 (2016), 2417-2450. Zbl 1383.35102, MR 3538418, 10.1088/0951-7715/29/8/2417; reference:[6] Fujie, K., Winkler, M., Yokota, T.: Blow-up prevention by logistic sources in a parabolic- elliptic Keller-Segel system with singular sensitivity.Nonlinear Anal., Theory Methods Appl., Ser. A 109 (2014), 56-71. Zbl 1297.35051, MR 3247293, 10.1016/j.na.2014.06.017; reference:[7] Fujie, K., Winkler, M., Yokota, T.: Boundedness of solutions to parabolic-elliptic Keller- Segel systems with signal-dependent sensitivity.Math. Methods Appl. Sci. 38 (2015), 1212-1224. Zbl 1329.35011, MR 3338145, 10.1002/mma.3149; reference:[8] Keller, E. F., Segel, L. A.: Initiation of slime mold aggregation viewed as an instability.J. Theor. Biol. 26 (1970), 399-415. Zbl 1170.92306, MR 3925816, 10.1016/0022-5193(70)90092-5; reference:[9] Kurt, H. I., Shen, W.: Finite-time blow-up prevention by logistic source in parabolic-elliptic chemotaxis models with singular sensitivity in any dimensional setting.SIAM J. Math. Anal. 53 (2021), 973-1003. Zbl 1455.35269, MR 4212880, 10.1137/20M1356609; reference:[10] Lankeit, J.: Eventual smoothness and asymptotics in a three-dimensional chemotaxis system with logistic source.J. Differ. Equations 258 (2015), 1158-1191. Zbl 1319.35085, MR 3294344, 10.1016/j.jde.2014.10.016; reference:[11] Lankeit, J., Winkler, M.: A generalized solution concept for the Keller-Segel system with logarithmic sensitivity: Global solvability for large nonradial data.NoDEA, Nonlinear Differ. Equ. Appl. 24 (2017), Article ID 49, 33 pages. Zbl 1373.35166, MR 3674184, 10.1007/s00030-017-0472-8; reference:[12] Nagai, T., Senba, T.: Behavior of radially symmetric solutions of a system related to chemotaxis.Nonlinear Anal., Theory Methods Appl. 30 (1997), 3837-3842. Zbl 0891.35014, MR 1602939, 10.1016/S0362-546X(96)00256-8; reference:[13] Osaki, K., Tsujikawa, T., Yagi, A., Mimura, M.: Exponential attractor for a chemotaxis-growth system of equations.Nonlinear Anal., Theory Methods Appl., Ser. A 51 (2002), 119-144. Zbl 1005.35023, MR 1915744, 10.1016/S0362-546X(01)00815-X; reference:[14] Osaki, K., Yagi, A.: Finite dimensional attractor for one-dimensional Keller-Segel equations.Funkc. Ekvacioj, Ser. Int. 44 (2001), 441-469. Zbl 1145.37337, MR 1893940; reference:[15] Stinner, C., Surulescu, C., Winkler, M.: Global weak solutions in a PDE-ODE system modeling multiscale cancer cell invasion.SIAM J. Math. Anal. 46 (2014), 1969-2007. Zbl 1301.35189, MR 3216646, 10.1137/13094058X; reference:[16] Tao, Y., Winkler, M.: Persistence of mass in a chemotaxis system with logistic source.J. Differ. Equations 259 (2015), 6142-6161. Zbl 1321.35084, MR 3397319, 10.1016/j.jde.2015.07.019; reference:[17] Tello, J. I., Winkler, M.: A chemotaxis system with logistic source.Commun. Partial Differ. Equations 32 (2007), 849-877. Zbl 1121.37068, MR 2334836, 10.1080/03605300701319003; reference:[18] Viglialoro, G.: Very weak global solutions to a parabolic-parabolic chemotaxis-system with logistic source.J. Math. Anal. Appl. 439 (2016), 197-212. Zbl 1386.35163, MR 3474358, 10.1016/j.jmaa.2016.02.069; reference:[19] Viglialoro, G.: Boundedness properties of very weak solutions to a fully parabolic chemotaxis-system with logistic source.Nonlinear Anal., Real World Appl. 34 (2017), 520-535. Zbl 1355.35094, MR 3567976, 10.1016/j.nonrwa.2016.10.001; reference:[20] Winkler, M.: Chemotaxis with logistic source: Very weak global solutions and their boundedness properties.J. Math. Anal. Appl. 348 (2008), 708-729. Zbl 1147.92005, MR 2445771, 10.1016/j.jmaa.2008.07.071; reference:[21] Winkler, M.: Aggregation vs. global diffusive behavior in the higher-dimensional Keller- Segel model.J. Differ. Equations 248 (2010), 2889-2905. Zbl 1190.92004, MR 2644137, 10.1016/j.jde.2010.02.008; reference:[22] Winkler, M.: Boundedness in the higher-dimensional parabolic-parabolic chemotaxis system with logistic source.Commun. Partial Differ. Equqtions 35 (2010), 1516-1537. Zbl 1290.35139, MR 2754053, 10.1080/03605300903473426; reference:[23] Winkler, M.: How strong singularities can be regularized by logistic degradation in the Keller-Segel system?.Ann. Mat. Pura Appl. (4) 198 (2019), 1615-1637. Zbl 1437.35004, MR 4022112, 10.1007/s10231-019-00834-z; reference:[24] Winkler, M.: The role of superlinear damping in the construction of solutions to drift-diffusion problems with initial data in $L^1$.Adv. Nonlinear Anal. 9 (2020), 526-566. Zbl 1419.35099, MR 3969152, 10.1515/anona-2020-0013; reference:[25] Winkler, M.: $L^1$ solutions to parabolic Keller-Segel systems involving arbitrary superlinear degradation.Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 24 (2023), 141-172. Zbl 7697296, MR 4587743, 10.2422/2036-2145.202005_016; reference:[26] Zhang, W.: Global generalized solvability in the Keller-Segel system with singular sensitivity and arbitrary superlinear degradation.Discrete Contin. Dyn. Syst., Ser. B 28 (2023), 1267-1278. Zbl 1502.35184, MR 4509358, 10.3934/dcdsb.2022121; reference:[27] Zhao, X.: Boundedness to a parabolic-parabolic singular chemotaxis system with logistic source.J. Differ. Equations 338 (2022), 388-414. Zbl 1497.92037, MR 4471552, 10.1016/j.jde.2022.08.003; reference:[28] Zhao, X., Zheng, S.: Global boundedness to a chemotaxis system with singular sensitivity and logistic source.Z. Angew. Math. Phys. 68 (2017), Article ID 2, 13 pages. Zbl 1371.35151, MR 3575592, 10.1007/s00033-016-0749-5; reference:[29] Zhao, X., Zheng, S.: Global existence and boundedness of solutions to a chemotaxis system with singular sensitivity and logistic-type source.J. Differ. Equations 267 (2019), 826-865. Zbl 1412.35177, MR 3957973, 10.1016/j.jde.2019.01.026

الاتاحة: http://hdl.handle.net/10338.dmlcz/152272

المؤلفون: Ishida, Sachiko, Yokota, Tomomi

مصطلحات موضوعية: keyword:stabilization, keyword:degenerate diffusion, keyword:Keller-Segel systems, msc:35B35, msc:35D30, msc:35Q92, msc:92C17

وصف الملف: application/pdf

Relation: mr:MR4563030; zbl:Zbl 07675588; reference:[1] Cao, X.: Global bounded solutions of the higher-dimensional Keller-Segel system under smallness conditions in optimal spaces.Discrete Contin. Dyn. Syst. 35 (2015), 1891–1904. MR 3294230, 10.3934/dcds.2015.35.1891; reference:[2] Cieślak, T., Stinner, C.: Finite-time blowup in a supercritical quasilinear parabolic-parabolic Keller-Segel system in dimension 2.Acta Appl. Math. 129 (2014), 135–146. Zbl 1295.35123, MR 3152080, 10.1007/s10440-013-9832-5; reference:[3] Cieślaka, T., Winkler, M.: Stabilization in a higher-dimensional quasilinear Keller-Segel system with exponentially decaying diffusivity and subcritical sensitivity.Nonlinear Anal. 159 (2017), 129–144. MR 3659827; reference:[4] Hashira, T., Ishida, S., Yokota, T.: Finite-time blow-up for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type.J. Differential Equations 264 (2018), 6459–6485. MR 3770055, 10.1016/j.jde.2018.01.038; reference:[5] Ishida, S., Seki, K., Yokota, T.: Boundedness in quasilinear Keller-Segel systems of parabolic-parabolic type on non-convex bounded domains.J. Differential Equations 256 (2014), 2993–3010. MR 3199754, 10.1016/j.jde.2014.01.028; reference:[6] Ishida, S., Yokota, T.: Boundedness in a quasilinear fully parabolic Keller-Segel system via maximal Sobolev regularity.Discrete Contin. Dyn. Syst. Ser. S 13 (2020), 212–232. MR 4043690; reference:[7] Ishida, S., Yokota, T.: Weak stabilization in degenerate parabolic equations in divergence form: application to degenerate Keller-Segel systems.Calc. Var. Partial Differential Equations 61 (2022), Paper No. 105. MR 4404850, 10.1007/s00526-022-02203-w; reference:[8] Jiang, J.: Convergence to equilibria of global solutions to a degenerate quasilinear Keller-Segel system.Z. Angew. Math. Phys. 69 (2018), Paper No. 130. MR 3856789, 10.1007/s00033-018-1025-7; reference:[9] Langlais, M., Phillips, D.: Stabilization of solutions of nonlinear and degenerate evolution equations.Nonlinear Anal. 9 (1985), 321–333. 10.1016/0362-546X(85)90057-4; reference:[10] Lankeit, J.: Infinite time blow-up of many solutions to a general quasilinear parabolic-elliptic Keller-Segel system.Discrete Contin. Dyn. Syst. Ser. S 13 (2020), 233–255. MR 4043691; reference:[11] Laurençot, P., Mizoguchi, N.: Finite time blowup for the parabolic-parabolic Keller-Segel system with critical diffusion.Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), 197–220. MR 3592684, 10.1016/j.anihpc.2015.11.002; reference:[12] Senba, T., Suzuki, T.: A quasi-linear parabolic system of chemotaxis.Abstr. Appl. Anal. 2006 (2006), 1–21. MR 2211660, 10.1155/AAA/2006/23061; reference:[13] Sugiyama, Y., Kunii, H.: Global existence and decay properties for a degenerate Keller-Segel model with a power factor in drift term.J. Differential Equations 227 (2006), 333–364. MR 2235324, 10.1016/j.jde.2006.03.003; reference:[14] Tao, Y., Winkler, M.: Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity.J. Differential Equations 252 (2012), 692–715. MR 2852223, 10.1016/j.jde.2011.08.019; reference:[15] Winkler, M.: Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model.J. Differential Equations 248 (2010), 2889–2905. Zbl 1190.92004, MR 2644137, 10.1016/j.jde.2010.02.008; reference:[16] Winkler, M.: Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system.J. Math. Pures Appl. 100 (2013), 748–767. Zbl 1326.35053, MR 3115832, 10.1016/j.matpur.2013.01.020

الاتاحة: http://hdl.handle.net/10338.dmlcz/151565

المؤلفون: Chiyo, Yutaro

مصطلحات موضوعية: keyword:chemotaxis, keyword:quasilinear, keyword:attraction-repulsion, keyword:stabilization, msc:35B40, msc:35K59, msc:92C17

وصف الملف: application/pdf

Relation: mr:MR4563028; zbl:Zbl 07675586; reference:[1] Chiyo, Y.: Stabilization for small mass in a quasilinear parabolic-elliptic-elliptic attraction-repulsion chemotaxis system with density-dependent sensitivity: repulsion-dominant case.Adv. Math. Sci. Appl. 31 (2) (2022), 327–341. MR 4521442; reference:[2] Chiyo, Y., Marras, M., Tanaka, Y., Yokota, T.: Blow-up phenomena in a parabolic-elliptic-elliptic attraction-repulsion chemotaxis system with superlinear logistic degradation.Nonlinear Anal. 212 (2021), 14 pp., Paper No. 112550. MR 4299101; reference:[3] Chiyo, Y., Yokota, T.: Stabilization for small mass in a quasilinear parabolic-elliptic-elliptic attraction-repulsion chemotaxis system with density-dependent sensitivity: balanced case.Matematiche (Catania), to appear.; reference:[4] Chiyo, Y., Yokota, T.: Boundedness and finite-time blow-up in a quasilinear parabolic-elliptic elliptic attraction-repulsion chemotaxis system.Z. Angew. Math. Phys. 73 (2) (2022), 27 pp., Paper No. 61. MR 4386024, 10.1007/s00033-022-01695-y; reference:[5] Fujie, K., Suzuki, T.: Global existence and boundedness in a fully parabolic 2D attraction-repulsion system: chemotaxis-dominant case.Adv. Math. Sci. Appl. 28 (2019), 1–9. MR 4416882; reference:[6] Ishida, S., Yokota, T.: Boundedness in a quasilinear fully parabolic Keller-Segel system via maximal Sobolev regularity.Discrete Contin. Dyn. Syst. Ser. S 13 (2020), 2112–232. MR 4043690; reference:[7] Ladyženskaja, O.A., Solonnikov, V.A., Ural’ceva, N.N.: Linear and Quasilinear Equations of Parabolic Type.AMS, Providence, 1968.; reference:[8] Lankeit, J.: Infinite time blow-up of many solutions to a general quasilinear parabolic-elliptic Keller-Segel system.Discrete Contin. Dyn. Syst. Ser. S 13 (2) (2020), 233–255. MR 4043691; reference:[9] Lankeit, J.: Finite-time blow-up in the three-dimensional fully parabolic attraction-dominated attraction-repulsion chemotaxis system.J. Math. Anal. Appl. 504 (2) (2021), 16 pp., Paper No. 125409. MR 4270582, 10.1016/j.jmaa.2021.125409; reference:[10] Li, Y., Lin, K., Mu, C.: Asymptotic behavior for small mass in an attraction-repulsion chemotaxis system.Electron. J. Differential Equations 2015 (146) (2015), 13 pp. MR 3358518; reference:[11] Lin, K., Mu, C., Wang, L.: Large-time behavior of an attraction-repulsion chemotaxis system.J. Math. Anal. Appl. 426 (1) (2015), 105–124. MR 3306365, 10.1016/j.jmaa.2014.12.052; reference:[12] Luca, M., Chavez-Ross, A., Edelstein-Keshet, L., Mogliner, A.: Chemotactic signalling, microglia, and Alzheimer’s disease senile plague: Is there a connection?.Bull. Math. Biol. 65 (2003), 673–730. 10.1016/S0092-8240(03)00030-2; reference:[13] Tao, Y., Wang, Z.-A.: Competing effects of attraction vs. repulsion in chemotaxis.Math. Models Methods Appl. Sci. 23 (2013), 1–36. MR 2997466, 10.1142/S0218202512500443; reference:[14] Tao, Y., Winkler, M.: Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity.J. Differential Equations 252 (1) (2012), 692–715. MR 2852223, 10.1016/j.jde.2011.08.019; reference:[15] Winkler, M.: Global classical solvability and generic infinite-time blow-up in quasilinear Keller-Segel systems with bounded sensitivities.J. Differential Equations 266 (12) (2019), 8034–8066. MR 3944248, 10.1016/j.jde.2018.12.019

الاتاحة: http://hdl.handle.net/10338.dmlcz/151563

المؤلفون: Tanaka, Yuya

مصطلحات موضوعية: keyword:degenerate Keller–Segel system, keyword:logistic source, msc:35B44, msc:35K65, msc:92C17

وصف الملف: application/pdf

Relation: mr:MR4563034; zbl:Zbl 07675592; reference:[1] Black, T., Fuest, M., Lankeit, J.: Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic-elliptic Keller-Segel systems.Z. Angew. Math. Phys. 72 (96) (2021), 23 pp. MR 4252274; reference:[2] Fuest, M.: Blow-up profiles in quasilinear fully parabolic Keller-Segel systems.Nonlinearity 33 (5) (2020), 2306–2334. MR 4105360, 10.1088/1361-6544/ab7294; reference:[3] Fuest, M.: Approaching optimality in blow-up results for Keller-Segel systems with logistic-type dampening.NoDEA Nonlinear Differential Equations Appl. 28 (16) (2021), 17 pp. MR 4223515; reference:[4] Ishida, S., Yokota, T.: Global existence of weak solutions to quasilinear degenerate Keller–Segel systems of parabolic–parabolic type.J. Differential Equations 252 (2) (2012), 1421–1440. MR 2853545, 10.1016/j.jde.2011.02.012; reference:[5] Ishida, S., Yokota, T.: Blow-up in finite or infinite time for quasilinear degenerate Keller–Segel systems of parabolic–parabolic type.Discrete Contin. Dyn. Syst. Ser. B 18 (10) (2013), 2569–2596. MR 3124753; reference:[6] Lankeit, J.: Locally bounded global solutions to a chemotaxis consumption model with singular sensitivity and nonlinear diffusion.J. Differential Equations 262 (7) (2017), 4052–4084. MR 3599425, 10.1016/j.jde.2016.12.007; reference:[7] Tanaka, Y.: Boundedness and finite-time blow-up in a quasilinear parabolic–elliptic chemotaxis system with logistic source and nonlinear production.J. Math. Anal. Appl. 506 (2022), 29 pp., no. 125654. MR 4315564, 10.1016/j.jmaa.2021.125654; reference:[8] Tanaka, Y., Yokota, T.: Finite-time blow-up in a quasilinear degenerate parabolic–elliptic chemotaxis system with logistic source and nonlinear production.Discrete Contin. Dyn. Syst. Ser. B 28 (1) (2023), 262–286. MR 4489725, 10.3934/dcdsb.2022075; reference:[9] Winkler, M.: Blow-up in a higher-dimensional chemotaxis system despite logistic growth restriction.J. Math. Anal. Appl. 384 (2) (2011), 261–272. MR 2825180, 10.1016/j.jmaa.2011.05.057; reference:[10] Winkler, M.: Finite-time blow-up in low-dimensional Keller–Segel systems with logistic-type superlinear degradation.Z. Angew. Math. Phys. 69 (69) (2018), 40 pp. MR 3772030; reference:[11] Winkler, M., Djie, K.C.: Boundedness and finite-time collapse in a chemotaxis system with volume-filling effect.Nonlinear Anal. 72 (2) (2010), 1044–1064. MR 2579368, 10.1016/j.na.2009.07.045

الاتاحة: http://hdl.handle.net/10338.dmlcz/151569

المؤلفون: Mizukami, Masaaki, Tanaka, Yuya

مصطلحات موضوعية: keyword:chemotaxis, keyword:Lotka–Volterra, keyword:finite-time blow-up, msc:35B44, msc:35K51, msc:92C17

وصف الملف: application/pdf

Relation: mr:MR4563033; zbl:Zbl 07675591; reference:[1] Baldelli, L., Filippucci, R.: A priori estimates for elliptic problems via Liouville type theorems.Discrete Contin. Dyn. Syst. Ser. S 13 (7) (2020), 1883–1898. MR 4097623; reference:[2] Black, T., Lankeit, J., Mizukami, M.: On the weakly competitive case in a two-species chemotaxis model.IMA J. Appl. Math. 81 (5) (2016), 860–876. MR 3556387, 10.1093/imamat/hxw036; reference:[3] Cieślak, T., Winkler, M.: Finite-time blow-up in a quasilinear system of chemotaxis.Nonlinearity 21 (5) (2008), 1057–1076. MR 2412327, 10.1088/0951-7715/21/5/009; reference:[4] Fuest, M.: Approaching optimality in blow-up results for Keller-Segel systems with logistic-type dampening.NoDEA Nonlinear Differential Equations Appl. 28 (16) (2021), 17 pp. MR 4223515; reference:[5] Mizukami, M.: Boundedness and stabilization in a two-species chemotaxis-competition system of parabolic-parabolic-elliptic type.Math. Methods Appl. Sci. 41 (1) (2018), 234–249. MR 3745368, 10.1002/mma.4607; reference:[6] Mizukami, M., Tanaka, Y., Yokota, T.: Can chemotactic effects lead to blow-up or not in two-species chemotaxis-competition models?.Z. Angew. Math. Phys. 73 (239) (2022), 25 pp. MR 4500792; reference:[7] Stinner, C., Tello, J.I., Winkler, M.: Competitive exclusion in a two-species chemotaxis model.J. Math. Biol. 68 (7) (2014), 1607–1626. MR 3201907, 10.1007/s00285-013-0681-7; reference:[8] Tello, J.I., Winkler, M.: Stabilization in a two-species chemotaxis system with a logistic source.Nonlinearity 25 (5) (2012), 1413–1425. MR 2914146, 10.1088/0951-7715/25/5/1413; reference:[9] Tu, X., Qiu, S.: Finite-time blow-up and global boundedness for chemotaxis system with strong logistic dampening.J. Math. Anal. Appl. 486 (1) (2020), 25 pp. MR 4053055; reference:[10] Winkler, M.: Finite-time blow-up in low-dimensional Keller-Segel systems with logistic-type superlinear degradation.Z. Angew. Math. Phys. 69 (69) (2018), 40 pp. MR 3772030

الاتاحة: http://hdl.handle.net/10338.dmlcz/151568

المؤلفون: Yang, Lu, Liu, Xi, Hou, Zhibo

مصطلحات موضوعية: keyword:Keller-Segel-Navier-Stokes, keyword:global solution, keyword:decay estimate, keyword:indirect process, msc:35B35, msc:35B40, msc:35K55, msc:35Q35, msc:92C17

وصف الملف: application/pdf

Relation: mr:MR4541089; zbl:Zbl 07655755; reference:[1] Bellomo, N., Bellouquid, A., Tao, Y., Winkler, M.: Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues.Math. Models Methods Appl. Sci. 25 (2015), 1663-1763. Zbl 1326.35397, MR 3351175, 10.1142/S021820251550044X; reference:[2] Cao, X.: Global bounded solutions of the higher-dimensional Keller-Segel system under smallness conditions in optimal spaces.Discrete Contin. Dyn. Syst. 35 (2015), 1891-1904. Zbl 06384058, MR 3294230, 10.3934/dcds.2015.35.1891; reference:[3] Cao, X., Lankeit, J.: Global classical small-data solutions for a three-dimensional chemotaxis Navier-Stokes system involving matrix-valued sensitivities.Calc. Var. Partial Differ. Equ. 55 (2016), Article ID 107, 39 pages. Zbl 1366.35075, MR 3531759, 10.1007/s00526-016-1027-2; reference:[4] Corrias, L., Perthame, B.: Asymptotic decay for the solutions of the parabolic-parabolic Keller-Segel chemotaxis system in critical spaces.Math. Comput. Modelling 47 (2008), 755-764. Zbl 1134.92006, MR 2404241, 10.1016/j.mcm.2007.06.005; reference:[5] Espejo, E., Suzuki, T.: Reaction terms avoiding aggregation in slow fluids.Nonlinear Anal., Real World Appl. 21 (2015), 110-126. Zbl 1302.35102, MR 3261583, 10.1016/j.nonrwa.2014.07.001; reference:[6] Fujie, K., Senba, T.: Application of an Adams type inequality to a two-chemical substances chemotaxis system.J. Differ. Equations 263 (2017), 88-148. Zbl 1364.35120, MR 3631302, 10.1016/j.jde.2017.02.031; reference:[7] Fujie, K., Senba, T.: Blowup of solutions to a two-chemical substances chemotaxis system in the critical dimension.J. Differ. Equations 266 (2019), 942-976. Zbl 1406.35149, MR 3906204, 10.1016/j.jde.2018.07.068; reference:[8] Hillen, T., Painter, K. J.: A user's guide to PDE models for chemotaxis.J. Math. Biol. 58 (2009), 183-217. Zbl 1161.92003, MR 2448428, 10.1007/s00285-008-0201-3; reference:[9] Horstmann, D.: From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I.Jahresber. Dtsch. Math.-Ver. 105 (2003), 103-165. Zbl 1071.35001, MR 2013508; reference:[10] Jin, H.-Y.: Boundedness of the attraction-repulsion Keller-Segel system.J. Math. Anal. Appl. 422 (2015), 1463-1478. Zbl 1307.35139, MR 3269523, 10.1016/j.jmaa.2014.09.049; reference:[11] Li, X., Xiao, Y.: Global existence and boundedness in a 2D Keller-Segel-Stokes system.Nonlinear Anal., Real World Appl. 37 (2017), 14-30. Zbl 1394.35241, MR 3648369, 10.1016/j.nonrwa.2017.02.005; reference:[12] Liu, J., Wang, Y.: Global weak solutions in a three-dimensional Keller-Segel-Navier-Stokes system involving a tensor-valued sensitivity with saturation.J. Differ. Equations 262 (2017), 5271-5305. Zbl 1377.35148, MR 3612542, 10.1016/j.jde.2017.01.024; reference:[13] Luca, M., Chavez-Ross, A., Edelstein-Keshet, L., Mogilner, A.: Chemotactic signaling, microglia, and Alzheimer's disease senile plagues: Is there a connection?.Bull. Math. Biol. 65 (2003), 693-730. Zbl 1334.92077, 10.1016/S0092-8240(03)00030-2; reference:[14] Nagai, T., Senba, T., Yoshida, K.: Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis.Funkc. Ekvacioj, Ser. Int. 40 (1997), 411-433. Zbl 0901.35104, MR 1610709; reference:[15] Osaki, K., Yagi, A.: Finite dimensional attractor for one-dimensional Keller-Segel equations.Funkc. Ekvacioj, Ser. Int. 44 (2001), 441-469. Zbl 1145.37337, MR 1893940; reference:[16] Tao, Y., Wang, Z.-A.: Competing effects of attraction vs. repulsion in chemotaxis.Math. Models Methods Appl. Sci. 23 (2013), 1-36. Zbl 1403.35136, MR 2997466, 10.1142/S0218202512500443; reference:[17] Tao, Y., Winkler, M.: Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis-fluid system.Z. Angew. Math. Phys. 66 (2015), 2555-2573. Zbl 1328.35084, MR 3412312, 10.1007/s00033-015-0541-y; reference:[18] Tao, Y., Winkler, M.: Blow-up prevention by quadratic degradation in a two-dimensional Keller-Segel-Navier-Stokes system.Z. Angew. Math. Phys. 67 (2016), Article ID 138, 23 pages. Zbl 1356.35054, MR 3562386, 10.1007/s00033-016-0732-1; reference:[19] Wang, Y.: Global weak solutions in a three-dimensional Keller-Segel-Navier-Stokes system with subcritical sensitivity.Math. Models Methods Appl. Sci. 27 (2017), 2745-2780. Zbl 1378.92010, MR 3723735, 10.1142/S0218202517500579; reference:[20] Wang, Y., Winkler, M., Xiang, Z.: Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity.Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 18 (2018), 421-466. Zbl 1395.92024, MR 3801284, 10.2422/2036-2145.201603_004; reference:[21] Wang, Y., Yang, L.: Boundedness in a chemotaxis-fluid system involving a saturated sensitivity and indirect signal production mechanism.J. Differ. Equations 287 (2021), 460-490. Zbl 1464.35052, MR 4242960, 10.1016/j.jde.2021.04.001; reference:[22] Winkler, M.: Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model.J. Differ. Equations 248 (2010), 2889-2905. Zbl 1190.92004, MR 2644137, 10.1016/j.jde.2010.02.008; reference:[23] Winkler, M.: Global large-data solutions in a chemotaxis-(Navier-)Stokes system modeling cellular swimming in fluid drops.Commun. Partial Differ. Equations 37 (2012), 319-351. Zbl 1236.35192, MR 2876834, 10.1080/03605302.2011.591865; reference:[24] Winkler, M.: A three-dimensional Keller-Segel-Navier-Stokes system with logistic source: Global weak solutions and asymptotic stabilization.J. Funct. Anal. 276 (2019), 1339-1401. Zbl 1408.35132, MR 3912779, 10.1016/j.jfa.2018.12.009; reference:[25] Winkler, M.: Small-mass solutions in the two-dimensional Keller-Segel system coupled to Navier-Stokes equations.SIAM J. Math. Anal. 52 (2020), 2041-2080. Zbl 1441.35079, MR 4091876, 10.1137/19M1264199; reference:[26] Winkler, M.: Reaction-driven relaxation in three-dimensional Keller-Segel-Navier-Stokes interaction.Commun. Math. Phys. 389 (2022), 439-489. Zbl 07463712, MR 4365145, 10.1007/s00220-021-04272-y; reference:[27] Yu, H., Wang, W., Zheng, S.: Global classical solutions to the Keller-Segel-Navier-Stokes system with matrix-valued sensitivity.J. Math. Anal. Appl. 461 (2018), 1748-1770. Zbl 1390.35381, MR 3765513, 10.1016/j.jmaa.2017.12.048; reference:[28] Yu, P.: Blow-up prevention by saturated chemotactic sensitivity in a 2D Keller-Segel-Stokes system.Acta Appl. Math. 169 (2020), 475-497. Zbl 1470.35185, MR 4146909, 10.1007/s10440-019-00307-8; reference:[29] Zhang, W., Niu, P., Liu, S.: Large time behavior in a chemotaxis model with logistic growth and indirect signal production.Nonlinear Anal., Real World Appl. 50 (2019), 484-497. Zbl 1435.35068, MR 3959244, 10.1016/j.nonrwa.2019.05.002

الاتاحة: http://hdl.handle.net/10338.dmlcz/151504

المؤلفون: Corbin, Gregor

مصطلحات موضوعية: glioblastoma, msc:65M08, kinetic equations, ddc:610, msc:92C17, ddc:510, haptotaxis, asymptotic-preserving, msc:35L04, msc:35-04, multi-scale model, numerics

وصف الملف: application/pdf

URL الوصول: https://explore.openaire.eu/search/publication?articleId=od_______651::ca056746265fb0d0415c5f21651bfa3b
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/6125

المؤلفون: Hintsche, Marius (M. Sc.)

مصطلحات موضوعية: Institut für Physik und Astronomie, ddc:530, msc:92C17

وصف الملف: application/pdf

URL الوصول: https://explore.openaire.eu/search/publication?articleId=od_______266::793fad11d654eea9a96bafac68ebcfa6
https://publishup.uni-potsdam.de/frontdoor/index/index/docId/42697

المؤلفون: Fujie, Kentarou, Senba, Takasi

مصطلحات موضوعية: keyword:Chemotaxis, global existence, Lyapunov functional, Adams’ inequality, msc:35B45, msc:35K45, msc:35Q92, msc:92C17

وصف الملف: application/pdf

Relation: reference:[1] Bellomo, N., Bellouquid, A., Tao, Y., Winkler, M.: Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues. Math. Models Methods Appl. Sci. 25 (2015), 1663–1763. MR 3351175, 10.1142/S021820251550044X; reference:[2] Biler, P., Karch, G., cot, P. Lauren\c, Nadzieja, T.: The $8\pi$-problem for radially symmetric solutions of a chemotaxis model in a disc. Topol. Methods Nonlinear Anal. 27 (2006), 133–147. MR 2236414; reference:[3] Biler, P., Nadzieja, T.: Existence and nonexistence of solutions for a model of gravitational interaction of particles. I. Colloq. Math. 66 (1994), 319–334. MR 1268074, 10.4064/cm-66-2-319-334; reference:[4] Cao, X.: Global bounded solutions of the higher-dimensional Keller-Segel system under smallness conditions in optimal spaces. Discrete Contin. Dyn. Syst. 35 (2015), 1891–1904. MR 3294230, 10.3934/dcds.2015.35.1891; reference:[5] Chang, S.Y.A., Yang, P.: Conformal deformation of metrics on $S^2$. J. Differential Geom. 27 (1988), 259–296. MR 0925123, 10.4310/jdg/1214441783; reference:[6] Fujie, K., Senba, T.: Global existence and boundedness in a parabolic-elliptic Keller-Segel system with general sensitivity. Discrete Contin. Dyn. Syst. Ser. B 21 (2016), 81–102. MR 3426833; reference:[7] Fujie, K., Senba, T.: Global existence and boundedness of radial solutions to a two dimensional fully parabolic chemotaxis system with general sensitivity. Nonlinearity 29 (2016), 2417–2450. MR 3538418, 10.1088/0951-7715/29/8/2417; reference:[8] Fujie, K., Senba, T.: Application of an Adams type inequality to a two-chemical substances chemotaxis system. J. Differential Equations 263 (2017), 88–148. MR 3631302, 10.1016/j.jde.2017.02.031; reference:[9] Fujie, K., Senba, T.: Blow-up of solutions to a two-chemical substances chemotaxis system in the critical dimension. In preparation. MR 3906204; reference:[10] Gajewski, H., Zacharias, K.: On a reaction-diffusion system modelling chemotaxis. International Conference on Differential Equations, Vol. 1, 2 (Berlin 1999), 1098–1103, World Sci. Publ., River Edge, NJ, 2000. MR 1870292; reference:[11] Herrero, M.A, Velázquez, J.J.L.: A blow-up mechanism for a chemotaxis model. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 24 (1997), 663–683. MR 1627338; reference:[12] Hillen, T., Painter, K.: A user’s guide to PDE models for chemotaxis. J. Math. Biol. 58 (2009), 183–217. MR 2448428, 10.1007/s00285-008-0201-3; reference:[13] Horstmann, D.: On the existence of radially symmetric blow-up solutions for the Keller-Segel model. J. Math. Biol. 44 (2002), 463–478. MR 1908133, 10.1007/s002850100134; reference:[14] Horstmann, D.: From 1970 until present: the Keller-Segel model in chemotaxis and its consequences. I. Jahresber. Deutsch. Math.-Verein. 105 (2003), 103–165. MR 2013508; reference:[15] Horstmann, D., Wang, G.: Blow-up in a chemotaxis model without symmetry assumptions. European J. Appl. Math. 12 (2001), 159–177. MR 1931303, 10.1017/S0956792501004363; reference:[16] J\"ager, W., Luckhaus, S.: On explosions of solutions to a system of partial differential equations modelling chemotaxis. Trans. Amer. Math. Soc. 329 (1992), 819–824. MR 1046835, 10.1090/S0002-9947-1992-1046835-6; reference:[17] Keller, E.F., Segel, L.A.: Initiation of slime mold aggregation viewed as an instability. J.Theor. Biol. 26 (1970), 399–415. MR 3925816, 10.1016/0022-5193(70)90092-5; reference:[18] Nagai, T.: Blow-up of radially symmetric solutions to a chemotaxis system. Adv. Math. Sci. Appl. 5 (1995), 581–601. MR 1361006; reference:[19] Nagai, T., Senba, T., Yoshida, K.: Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis. Funkc. Ekvacioj, Ser. Int. 40 (1997), 411–433. MR 1610709; reference:[20] Osaki, K., Yagi, A.: Finite dimensional attractor for one-dimensional Keller-Segel equations. Funkcial. Ekvac. 44 (2001), 441–469. MR 1893940; reference:[21] Ruf, B., Sani, F.: Sharp Adams-type inequalities in $\Bbb R^n$. Trans. Amer. Math. Soc. 365 (2013), 645–670. MR 2995369, 10.1090/S0002-9947-2012-05561-9; reference:[22] Sugiyama, Y.: On $\varepsilon$-regularity theorem and asymptotic behaviors of solutions for Keller-Segel systems. SIAM J. Math. Anal. 41 (2009), 1664–1692. MR 2556579, 10.1137/080721078; reference:[23] Senba, T., Suzuki, T.: Chemotactic collapse in a parabolic-elliptic system of mathematical biology. Adv. Differential Equations 6 (2001), 21–50. MR 1799679; reference:[24] Tarsi, C.: Adams’ inequality and limiting Sobolev embeddings into Zygmund spaces. Potential Anal. 37 (2012), 353–385. MR 2988207, 10.1007/s11118-011-9259-4; reference:[25] Winkler, M.: Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system. J. Math. Pures Appl. 100 (2013), 748–767. MR 3115832, 10.1016/j.matpur.2013.01.020

الاتاحة: http://hdl.handle.net/10338.dmlcz/703047

المؤلفون: Senba, Takasi, Fujie, Kentarou

مصطلحات موضوعية: keyword:Chemotaxis system, nonlinear sensitivity, time-global existence, msc:35B45, msc:35K45, msc:35Q92, msc:92C17

وصف الملف: application/pdf

Relation: reference:[1] Fujie, K.: Boundedness in a fully parabolic chemotaxis system with singular sensitivity., J. Math. Anal. Appl., 424 (2015), pp. 675–684. MR 3286587, 10.1016/j.jmaa.2014.11.045; reference:[2] Fujie, K., Senba, T.: Global existence and boundedness in a parabolic-elliptic Keller-Segel system with general sensitivity., Discrete Contin. Dyn. Syst. Ser. B, 21 (2016), pp. 81–102. MR 3426833; reference:[3] Fujie, K., T., Senba: Global existence and boundedness of radial solutions to a two dimensional fully parabolic chemotaxis system with general sensitivity., Nonlinearity, 29 (2016), pp. 2417–2450. MR 3538418, 10.1088/0951-7715/29/8/2417; reference:[4] Fujie, K., Senba, T.: A sufficient condition of sensitivity functions for boundedness of solutions to a parabolic-parabolic chemotaxis system., Preprint. MR 3816648; reference:[5] Fujie, K., Yokota, T.: Boundedness in a fully parabolic chemotaxis system with strongly singular sensitivity., Appl. Math. Lett, 38 (2014), pp. 140–143. MR 3258217, 10.1016/j.aml.2014.07.021; reference:[6] Horstmann, D., Wang, G.: Blow-up in a chemotaxis model without symmetry assumptions., European J. Appl. Math., 12 (2001), pp. 159–177. MR 1931303, 10.1017/S0956792501004363; reference:[7] Mizoguchi, N., Winkler, M.: Is finite-time blow-up a generic phenomenon in the twodimensional Keller-Segel system?., Preprint.; reference:[8] Mora, X.: Semilinear parabolic problems define semiflows on $C^k$ spaces., Trans. Amer. Math.Soc, 278 (1983), pp. 21–55. MR 0697059; reference:[9] Nagai, T.: Blow-up of radially symmetric solutions to a chemotaxis system., Adv. Math. Sci. Appl. 5 (1995), pp. 581–601. MR 1361006; reference:[10] Nagai, T., Senba, T., Yoshida, K.: Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis., Funkcial. Ekvac., 40 (1997), pp. 411-433. MR 1610709; reference:[11] Nagai, T., Senba, T.: Global existence and blow-up of radial solutions to a parabolic-elliptic system of chemotaxis., Adv. Math. Sci. Appl, 8 (1998), pp. 145–156. MR 1623326; reference:[12] Quittner, P., Souplet, P.: Superlinear parabolic problems., Birkhäuser advanced text Basler Lehrbücher. Birkhäuser, Berlin, 2007. MR 2346798; reference:[13] Stinner, C., Winkler, M.: Global weak solutions in a chemotaxis system with large singular sensitivity., Nonlinear Analysis: Real World Applications, 12 (2011), pp. 3727–3740. MR 2833007; reference:[14] Winkler, M.: Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segelmodel., J. Differential Equations, 248 (2010), pp. 2889–2905. MR 2644137, 10.1016/j.jde.2010.02.008; reference:[15] Winkler, W.: Global solutions in a fully parabolic chemotaxis system with singular sensitivity., Math. Methods Appl. Sci., 34 (2011), pp. 176–190. MR 2778870, 10.1002/mma.1346; reference:[16] Winkler, M.: Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system., J. Math. Pures Appl., 100 (2013), pp. 748–767. MR 3115832, 10.1016/j.matpur.2013.01.020

الاتاحة: http://hdl.handle.net/10338.dmlcz/703026

المؤلفون: Mizukami, Masaaki

مصطلحات موضوعية: keyword:Chemotaxis, signal-dependent sensitivity, logistic term, global existence, msc:35A01, msc:35K51, msc:92C17

وصف الملف: application/pdf

Relation: reference:[1] Bellomo, N., Bellouquid, A., Tao, Y., Winkler, M.: Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues., Math. Models Methods Appl. Sci., 25, pp. 1663–1763, 2015. MR 3351175, 10.1142/S021820251550044X; reference:[2] Cao, X.: Global bounded solutions of the higher-dimensional Keller–Segel system under smallness conditions in optimal spaces., Discrete Contin. Dyn. Syst., 35, pp. 1891–1904, 2015. MR 3294230, 10.3934/dcds.2015.35.1891; reference:[3] Fujie, K.: Boundedness in a fully parabolic chemotaxis system with singular sensitivity., J.Math. Anal. Appl., 424, pp. 675–684, 2015. MR 3286587, 10.1016/j.jmaa.2014.11.045; reference:[4] Fujie, K.: Study of reaction-diffusion systems modeling chemotaxis., PhD thesis, Tokyo University of Science, 2016.; reference:[5] Fujie, K., Senba, T.: Global existence and boundedness of radial solutions to a two dimensional fully parabolic chemotaxis system with general sensitivity., Nonlinearity, 29, pp. 2417–2450, 2016. MR 3538418, 10.1088/0951-7715/29/8/2417; reference:[6] Fujie, K., Senba, T.: A sufficient condition of sensitivity functions for boundedness of solutions to a parabolic-parabolic chemotaxis system., preprint. MR 3816648; reference:[7] He, X., Zheng, S.: Convergence rate estimates of solutions in a higher dimensional chemotaxis system with logistic source., J. Math. Anal. Appl., 436, pp. 970–982, 2016. MR 3446989, 10.1016/j.jmaa.2015.12.058; reference:[8] Horstmann, D., Wang, G.: Blow-up in a chemotaxis model without symmetry assumptions., Eur. J. Appl. Math., 12, pp. 159–177, 2001. MR 1931303, 10.1017/S0956792501004363; reference:[9] Lankeit, J.: A new approach toward boundedness in a two-dimensional parabolic chemotaxis system with singular sensitivity., Math. Methods Appl. Sci., 39, pp. 394–404, 2016. MR 3454184, 10.1002/mma.3489; reference:[10] Lankeit, J., Winkler, M.: A generalized solution concept for the Keller–Segel system with logarithmic sensitivity: global solvability for large nonradial data., NoDEA, Nonlinear Differ. Equ. Appl., 24, No. 4, Paper No. 49, 33 p., 2017. MR 3674184, 10.1007/s00030-017-0472-8; reference:[11] Mizukami, M.: Boundedness and asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity., Discrete Contin. Dyn. Syst. Ser. B, 22, pp. 2301–2319, 2017. MR 3664704; reference:[12] Mizukami, M.: Improvement of conditions for asymptotic stability in a two-species chemotaxis competition model with signal-dependent sensitivity., submitted, arXiv:1706.04774[math.AP]. MR 3664704; reference:[13] Mizukami, M., Yokota, T.: Global existence and asymptotic stability of solutions to a two-species chemotaxis system with any chemical diffusion., J. Differential Equations, 261, pp. 2650–2669, 2016. MR 3507983, 10.1016/j.jde.2016.05.008; reference:[14] Mizukami, M., Yokota, T.: A unified method for boundedness in fully parabolic chemotaxis systems with signal-dependent sensitivity., Math. Nachr., to appear. MR 3722501; reference:[15] Nagai, T., Senba, T., Yoshida, K.: Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis., Funkcial. Ekvac., 40, pp. 411–433, 1997. MR 1610709; reference:[16] Negreanu, M., Tello, J. I.: On a two species chemotaxis model with slow chemical diffusion., SIAM J. Math. Anal., 46, pp. 3761–3781, 2014. MR 3277217, 10.1137/140971853; reference:[17] Negreanu, M., Tello, J. I.: Asymptotic stability of a two species chemotaxis system with non-diffusive chemoattractant., J. Differential Equations, 258, pp. 1592–1617, 2015. MR 3295594, 10.1016/j.jde.2014.11.009; reference:[18] Winkler, M.: Aggregation vs. global diffusive behavior in the higher-dimensional Keller–Segel model., J. Differential Equations, 248, pp. 2889–2905, 2010. MR 2644137, 10.1016/j.jde.2010.02.008; reference:[19] Winkler, M.: Global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening., J. Differential Equations, 257, pp. 1056–1077, 2014. MR 3210023, 10.1016/j.jde.2014.04.023; reference:[20] Zhang, Q., Li, X.: Global existence and asymptotic properties of the solution to a two-species chemotaxis system., J. Math. Anal. Appl., 418, pp. 47–63, 2014. MR 3198865, 10.1016/j.jmaa.2014.03.084

الاتاحة: http://hdl.handle.net/10338.dmlcz/703018

المؤلفون: Hirata, Misaki, Kurima, Shunsuke, Mizukami, Masaaki, Yokota, Tomomi

مصطلحات موضوعية: keyword:Chemotaxis, Navier–Stokes, Lotka–Volterra, large-time behaviour, msc:35B40, msc:35K55, msc:35Q30, msc:92C17

وصف الملف: application/pdf

Relation: reference:[1] Bellomo, N., Bellouquid, A., Tao, Y., Winkler, M.: Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues., Math. Models Methods Appl. Sci., 25 (2015), pp. 1663–1763. MR 3351175, 10.1142/S021820251550044X; reference:[2] Cao, X., Kurima, S., Mizukami, M.: Global existence and asymptotic behavior of classical solutions for a 3D two-species chemotaxis-Stokes system with competitive kinetics., arXiv: 1703.01794 [math.AP]. MR 3805111; reference:[3] Cao, X., Kurima, S., Mizukami, M.: Global existence and asymptotic behavior of classical solutions for a 3D two-species Keller–Segel-Stokes system with competitive kinetics., arXiv: 1706.07910 [math.AP]. MR 3805111; reference:[4] Hirata, M., Kurima, S., Mizukami, M., Yokota, T.: Boundedness and stabilization in a two-dimensional two-species chemotaxis-Navier–Stokes system with competitive kinetics., J. Differential Equations, 263 (2017), pp. 470–490. MR 3631313, 10.1016/j.jde.2017.02.045; reference:[5] Lankeit, J.: Long-term behaviour in a chemotaxis-fluid system with logistic source., Math. Models Methods Appl. Sci., 26 (2016), pp. 2071–2109. MR 3556640, 10.1142/S021820251640008X; reference:[6] Tao, Y., Winkler, M.: Blow-up prevention by quadratic degradation in a two-dimensional Keller–Segel-Navier–Stokes system., Z. Angew. Math. Phys., 67 (2016), Article 138. MR 3562386

الاتاحة: http://hdl.handle.net/10338.dmlcz/703017

المؤلفون: Christian Stinner, Christina Surulescu, Michael Winkler

المصدر: SIAM Journal on Mathematical Analysis. 46:1969-2007

مصطلحات موضوعية: delay, Quantitative Biology::Tissues and Organs, Integrin, Nanotechnology, msc:35K57, Haptotaxis, Quantitative Biology::Cell Behavior, Matrix (mathematics), msc:35Q92, asymptotic behavior, msc:92C17, ddc:510, chemotaxis, haptotaxis, Mathematics, biology, Applied Mathematics, Dynamics (mechanics), Mathematical analysis, Ode, Function (mathematics), Connection (mathematics), Computational Mathematics, Ordinary differential equation, biology.protein, msc:35B40, multiscale model, Biological system, Analysis

وصف الملف: application/pdf

URL الوصول: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9d919d1ecd1c4bfc6491a6114e5a07ab
https://doi.org/10.1137/13094058x

المؤلفون: Stinner, Christian, Surulescu, Christina, Uatay, Aydar

مصطلحات موضوعية: delay, Quantitative Biology::Tissues and Organs, Physics::Medical Physics, msc:35K57, go-or-grow, Quantitative Biology::Cell Behavior, tumor cell invasion, msc:35Q92, msc:35B40, multiscale model, asymptotic behavior, msc:92C17, ddc:510, haptotaxis

وصف الملف: application/pdf

URL الوصول: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::1668e660c944903f9a32d652cf7608c8
https://kluedo.ub.rptu.de/frontdoor/index/index/docId/4294

المؤلفون: Zhigun, Anna (Dr.), Surulescu, Christina (Prof. Dr.), Hunt, Alexander

مصطلحات موضوعية: global existence, go-or-grow dichotomy, Quantitative Biology::Tissues and Organs, Physics::Medical Physics, msc:35K59, weak solution, msc:35K57, Quantitative Biology::Cell Behavior, msc:35K51, Mathematics - Analysis of PDEs, msc:35K65, msc:35Q92, msc:35K20, FOS: Mathematics, cancer cell invasion, msc:92C17, ddc:510, parabolic system, haptotaxis, msc:35B45, degenerate diffusion, 35B45, 35D30, 35K20, 35K51, 35K57, 35K59, 35K65, 35Q92, 92C17, msc:35D30, Analysis of PDEs (math.AP)

وصف الملف: application/pdf

URL الوصول: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::94639f84e94885d7a59b5c43dde328ed

المؤلفون: Sandesh Athni Hiremath, Anna Zhigun, Christina Surulescu, Stefanie Sonner

المصدر: Hiremath, S A, Surulescu, C, Zhigun, A & Sonner, S 2018, ' On a coupled sde-PDE system modeling ACID-mediated tumor invasion ', Discrete and Continuous Dynamical Systems-Series B, vol. 23, no. 6, pp. 2339-2369 . https://doi.org/10.3934/dcdsb.2018071

مصطلحات موضوعية: 0301 basic medicine, Applied Mathematics, Quantitative Biology::Tissues and Organs, Dynamics (mechanics), Tumor cells, msc:35K59, Systems modeling, Biology, Quantitative Biology::Cell Behavior, 03 medical and health sciences, Stochastic differential equation, msc:60H10, 030104 developmental biology, Extracellular, Biophysics, Discrete Mathematics and Combinatorics, msc:92C17, ddc:510, Intracellular, Simulation

وصف الملف: application/pdf

URL الوصول: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::00a2519498bf9b28986c580fd714025b
https://kluedo.ub.uni-kl.de/files/4451/sde_pde_model15.pdf

المؤلفون: Liu, Ji, Zheng, Jia-Shan

مصطلحات موضوعية: keyword:boundedness, keyword:chemotaxis, keyword:nonlinear logistic source, msc:35K59, msc:92C17

وصف الملف: application/pdf

Relation: mr:MR3441339; zbl:Zbl 06537714; reference:[1] Cao, X.: Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with logistic source.J. Math. Anal. Appl. 412 (2014), 181-188. MR 3145792, 10.1016/j.jmaa.2013.10.061; reference:[2] Cieślak, T., Stinner, C.: Finite-time blowup in a supercritical quasilinear parabolic-parabolic Keller-Segel system in dimension 2.Acta Appl. Math. 129 (2014), 135-146. Zbl 1295.35123, MR 3152080, 10.1007/s10440-013-9832-5; reference:[3] Cieślak, T., Stinner, C.: Finite-time blowup and global-in-time unbounded solutions to a parabolic-parabolic quasilinear Keller-Segel system in higher dimensions.J. Differ. Equations 252 (2012), 5832-5851. Zbl 1252.35087, MR 2902137, 10.1016/j.jde.2012.01.045; reference:[4] Herrero, M. A., Velázquez, J. J. L.: A blow-up mechanism for a chemotaxis model.Ann. Sc. Norm. Super. Pisa Cl. Sci. 4. 24 (1997), 633-683. Zbl 0904.35037, MR 1627338; reference:[5] Horstmann, D., Wang, G.: Blow-up in a chemotaxis model without symmetry assumptions.Eur. J. Appl. Math. 12 (2001), 159-177. Zbl 1017.92006, MR 1931303, 10.1017/S0956792501004363; reference:[6] Horstmann, D., Winkler, M.: Boundedness vs. blow-up in a chemotaxis system.J. Differ. Equations 215 (2005), 52-107. Zbl 1085.35065, MR 2146345, 10.1016/j.jde.2004.10.022; reference:[7] Keller, E. F., Segel, L. A.: Initiation of slime mold aggregation viewed as an instability.J. Theor. Biol. 26 (1970), 399-415. Zbl 1170.92306, 10.1016/0022-5193(70)90092-5; reference:[8] Nagai, T., Senba, T., Yoshida, K.: Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis.Funkc. Ekvacioj. Ser. Int. 40 (1997), 411-433. Zbl 0901.35104, MR 1610709; reference:[9] Osaki, K., Yagi, A.: Finite dimensional attractor for one-dimensional Keller-Segel equations.Funkc. Ekvacioj. Ser. Int. 44 (2001), 441-469. Zbl 1145.37337, MR 1893940; reference:[10] Painter, K. J., Hillen, T.: Volume-filling and quorum-sensing in models for chemosensitive movement.Can. Appl. Math. Q. 10 (2002), 501-543. Zbl 1057.92013, MR 2052525; reference:[11] Tao, Y., Winkler, M.: Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity.J. Differ. Equations 252 (2012), 692-715. MR 2852223, 10.1016/j.jde.2011.08.019; reference:[12] Winkler, M.: Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system.J. Math. Pures Appl. 100 (2013), 748-767. Zbl 1326.35053, MR 3115832, 10.1016/j.matpur.2013.01.020; reference:[13] Winkler, M.: Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model.J. Differ. Equations 248 (2010), 2889-2905. Zbl 1190.92004, MR 2644137, 10.1016/j.jde.2010.02.008; reference:[14] Winkler, M.: Boundedness in the higher-dimensional parabolic-parabolic chemotaxis system with logistic source.Commun. Partial Differ. Equations 35 (2010), 1516-1537. Zbl 1290.35139, MR 2754053, 10.1080/03605300903473426

الاتاحة: http://hdl.handle.net/10338.dmlcz/144796

المؤلفون: Christina Surulescu, Anna Zhigun, Aydar Uatay

مصطلحات موضوعية: General Mathematics, Quantitative Biology::Tissues and Organs, General Physics and Astronomy, msc:35K59, msc:35K57, 01 natural sciences, Haptotaxis, Quantitative Biology::Cell Behavior, msc:35K51, Mathematics - Analysis of PDEs, msc:35Q92, FOS: Mathematics, medicine, 0101 mathematics, msc:92C17, ddc:510, parabolic system, haptotaxis, 35B45, 35D30, 35K20, 35K51, 35K57, 35K59, 35K65, 35Q92, 92C17, msc:35D30, Strongly coupled, Degenerate diffusion, Physics, global existence, Applied Mathematics, Weak solution, 010102 general mathematics, Degenerate energy levels, Cancer, weak solution, medicine.disease, 010101 applied mathematics, Parabolic system, Classical mechanics, msc:35K65, msc:35K20, cancer cell invasion, msc:35B45, degenerate diffusion, Analysis of PDEs (math.AP)

وصف الملف: application/pdf

URL الوصول: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8be14d9e680cdcfaf2faa60be1178ef0
https://kluedo.ub.rptu.de/files/4232/ZSU_hapto.pdf

المؤلفون: Fujie, Kentarou, Yokota, Tomomi

مصطلحات موضوعية: keyword:chemotaxis, keyword:global existence, keyword:boundedness, msc:35A01, msc:35B40, msc:35B45, msc:35K60, msc:35M33, msc:92C17

وصف الملف: application/pdf

Relation: mr:MR3306853; zbl:Zbl 06433687; reference:[1] Biler, P.: Global solutions to some parabolic-elliptic systems of chemotaxis.Adv. Math. Sci. Appl. 9 (1999), 347-359. Zbl 0941.35009, MR 1690388; reference:[2] Biler, P.: Local and global solvability of some parabolic systems modelling chemotaxis.Adv. Math. Sci. Appl. 8 (1998), 715-743. Zbl 0913.35021, MR 1657160; reference:[3] Fujie, K., Winkler, M., Yokota, T.: Boundedness of solutions to parabolic-elliptic Keller-Segel systems with signal-dependent sensitivity.(to appear) in Math. Methods Appl. Sci. DOI:10.1002/mma.3149. 10.1002/mma.3149; reference:[4] Hillen, T., Painter, K. J.: A user's guide to PDE models for chemotaxis.J. Math. Biol. 58 (2009), 183-217. Zbl 1161.92003, MR 2448428, 10.1007/s00285-008-0201-3; reference:[5] Horstmann, D., Winkler, M.: Boundedness vs. blow-up in a chemotaxis system.J. Differ. Equations 215 (2005), 52-107. Zbl 1085.35065, MR 2146345, 10.1016/j.jde.2004.10.022; reference:[6] Keller, E. F., Segel, L. A.: Traveling bands of chemotactic bacteria: A theoretical analysis.J. Theor. Biol. 30 (1971), 235-248. Zbl 1170.92308, 10.1016/0022-5193(71)90051-8; reference:[7] Keller, E. F., Segel, L. A.: Initiation of slime mold aggregation viewed as an instability.J. Theor. Biol. 26 (1970), 399-415. Zbl 1170.92306, 10.1016/0022-5193(70)90092-5; reference:[8] Manásevich, R., Phan, Q. H., Souplet, P.: Global existence of solutions for a chemotaxis-type system arising in crime modelling.Eur. J. Appl. Math. 24 (2013), 273-296. Zbl 1284.35445, MR 3031780, 10.1017/S095679251200040X; reference:[9] Mu, C., Wang, L., Zheng, P., Zhang, Q.: Global existence and boundedness of classical solutions to a parabolic-parabolic chemotaxis system.Nonlinear Anal., Real World Appl. 14 (2013), 1634-1642. Zbl 1261.35072, MR 3004526; reference:[10] Nagai, T., Senba, T.: Global existence and blow-up of radial solutions to a parabolic-elliptic system of chemotaxis.Adv. Math. Sci. Appl. 8 (1998), 145-156. Zbl 0902.35010, MR 1623326; reference:[11] Negreanu, M., Tello, J. I.: On a parabolic-elliptic chemotactic system with non-constant chemotactic sensitivity.Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 80 (2013), 1-13. Zbl 1260.35238, MR 3010749, 10.1016/j.na.2012.12.004; reference:[12] Osaki, K., Tsujikawa, T., Yagi, A., Mimura, M.: Exponential attractor for a chemotaxis- growth system of equations.Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 51 (2002), 119-144. Zbl 1005.35023, MR 1915744, 10.1016/S0362-546X(01)00815-X; reference:[13] Osaki, K., Yagi, A.: Global existence for a chemotaxis-growth system in $\mathbb R^2$.Adv. Math. Sci. Appl. 12 (2002), 587-606. MR 1943982; reference:[14] Othmer, H. G., Stevens, A.: Aggregation, blowup, and collapse: The ABC's of taxis in reinforced random walks.SIAM J. Appl. Math. 57 (1997), 1044-1081. Zbl 0990.35128, MR 1462051, 10.1137/S0036139995288976; reference:[15] Sleeman, B. D., Levine, H. A.: Partial differential equations of chemotaxis and angiogenesis.Applied mathematical analysis in the last century Math. Methods Appl. Sci. 24 (2001), 405-426. Zbl 0990.35014, MR 1821934, 10.1002/mma.212; reference:[16] Stinner, C., Winkler, M.: Global weak solutions in a chemotaxis system with large singular sensitivity.Nonlinear Anal., Real World Appl. 12 (2011), 3727-3740. Zbl 1268.35072, MR 2833007; reference:[17] Winkler, M.: Global solutions in a fully parabolic chemotaxis system with singular sensitivity.Math. Methods Appl. Sci. 34 (2011), 176-190. Zbl 1291.92018, MR 2778870, 10.1002/mma.1346; reference:[18] Winkler, M.: Absence of collapse in a parabolic chemotaxis system with signal-dependent sensitivity.Math. Nachr. 283 (2010), 1664-1673. Zbl 1205.35037, MR 2759803, 10.1002/mana.200810838; reference:[19] Winkler, M.: Boundedness in the higher-dimensional parabolic-parabolic chemotaxis system with logistic source.Commun. Partial Differ. Equations 35 (2010), 1516-1537. Zbl 1290.35139, MR 2754053, 10.1080/03605300903473426

الاتاحة: http://hdl.handle.net/10338.dmlcz/144140