Academic Journal
Boundedness in a quasilinear parabolic-parabolic chemotaxis system with nonlinear logistic source
| العنوان: | Boundedness in a quasilinear parabolic-parabolic chemotaxis system with nonlinear logistic source |
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| المؤلفون: | Liu, Ji, Zheng, Jia-Shan |
| بيانات النشر: | Institute of Mathematics, Academy of Sciences of the Czech Republic Matematický ústav AV ČR |
| سنة النشر: | 2015 |
| المجموعة: | DML-CZ (Czech Digital Mathematics Library) |
| مصطلحات موضوعية: | keyword:boundedness, keyword:chemotaxis, keyword:nonlinear logistic source, msc:35K59, msc:92C17 |
| الوصف: | summary:We study a quasilinear parabolic-parabolic chemotaxis system with nonlinear logistic source, under homogeneous Neumann boundary conditions in a smooth bounded domain. By establishing proper a priori estimates we prove that, with both the diffusion function and the chemotaxis sensitivity function being positive, the corresponding initial boundary value problem admits a unique global classical solution which is uniformly bounded. The result of this paper is a generalization of that of Cao (2014). |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 0011-4642 1572-9141 |
| 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 |
| Rights: | access:Unrestricted ; rights:DML-CZ Czech Digital Mathematics Library, http://dml.cz/ ; rights:Institute of Mathematics AS CR, http://www.math.cas.cz/ ; conditionOfUse:http://dml.cz/use |
| رقم الانضمام: | edsbas.651F757E |
| قاعدة البيانات: | BASE |
Full Text Finder | تدمد: | 00114642 15729141 |
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