المؤلفون: Ma, Li

مصطلحات موضوعية: keyword:Bochner formula, keyword:heat equation, keyword:global solution, keyword:stochastic completeness, keyword:porous-media equation, keyword:McKean type estimate, msc:05C50, msc:35Jxx, msc:53Cxx, msc:58J35, msc:68R10

وصف الملف: application/pdf

Relation: mr:MR4483052; zbl:Zbl 07584089; reference:[1] Bauer, F., Horn, P., Yong, Lin, Lippner, G., Mangoubi, D., Shing-Tung, Yau: Li-Yau inequality on graphs.J. Differential Geom. 99 (3) (2015), 359–405. MR 3316971, 10.4310/jdg/1424880980; reference:[2] Chavel, I., Karp, L.: Large time behavior of the heat kernel: the parabolic-potential alternative.Comment. Math. Helv. 66 (4) (1991), 541–556, DOI 10.1007/BF02566664. MR 1129796, 10.1007/BF02566664; reference:[3] Chung, F.R.K.: Spectral graph theory.CBMS Regional Conf. Ser. in Math., 1997. xii+207 pp. ISBN: 0-8218-0315-8. MR 1421568; reference:[4] Haeseler, S., Keller, M., Lenz, D., Wojciechowski, R.: Laplacians on infinite graphs: Dirichlet and Neumann boundary conditions.J. Spectr. Theory 2 (4) (2012), 397–432. MR 2947294, 10.4171/JST/35; reference:[5] Horn, P., Yong, Lin, Shuang, Liu, Shing-Tung, Yau: Volume doubling, Poincaré inequality and Gaussian heat kernel estimate for non-negatively curved graphs.arXiv:1411. 5087v4. MR 4036571; reference:[6] Ji, L., Mazzeo, R., Sesum, N.: Ricci flow on surfaces with cusps.Math. Ann. 345 (2009), 819–834. MR 2545867, 10.1007/s00208-009-0377-x; reference:[7] Keller, M., Lenz, D.: Unbounded Laplacians on graphs: basic spectral properties and the heat equation.Math. Model. Nat. Phenom. 5 (4) (2010), 198–224. MR 2662456, 10.1051/mmnp/20105409; reference:[8] Lin, Y., Liu, S.: Equivalent properties of CD inequality on grap.arXiv:1512.02677, 2015. MR 4545901; reference:[9] Lin, Y., Yau, S.T.: Ricci curvature and eigen-value estimate on locally finite graphs.Math. Res. Lett. 17 (2010), 343–356. MR 2644381, 10.4310/MRL.2010.v17.n2.a13; reference:[10] Ma, L.: Harnack’s inequality and Green’s functions on locally finite graphs.Nonlinear Anal. 170 (2018), 226–237. MR 3765562; reference:[11] Ma, L., Wang, X.Y.: Kato’s inequality and Liouville theorems on locally finite graphs.Sci. China Math. 56 (4) (2013), 771–776. MR 3034839, 10.1007/s11425-013-4577-1; reference:[12] Ma, L., Witt, I.: Discrete Morse flow for the Ricci flow and porous media equation.Commun. Nonlinear Sci. Numer. Simul. 59 (2018), 158–164. MR 3758379, 10.1016/j.cnsns.2017.11.002; reference:[13] Weber, A.: Analysis of the physical Laplacian and the heat flow on a locally finite graph.J. Math. Anal. Appl. 370 (1) (2010), 146–158. MR 2651136, 10.1016/j.jmaa.2010.04.044; reference:[14] Wojciechowski, R.K.: Heat kernel and essential spectrum of infinite graphs.Indiana Univ. Math. J. 58 (3) (2009), 1419–1441. MR 2542093, 10.1512/iumj.2009.58.3575

الاتاحة: http://hdl.handle.net/10338.dmlcz/150663