[1] Bauer F, Hua B, Jost J. The dual cheeger constant and spectra of infinite graphs. Adv Math, 2014, 251(2):147-194 [2] Bebernes J, Eberly D. Mathematical Problems from Combustion Theory. New York:Springer, 1989 [3] Chung F R K. Spectral Graph Theory, CBMS Reg Conf Ser Math. Providence, RI:Amer Math Soc, 1997 [4] Chung Y S, Lee Y S, Chung S Y. Extinction and positivity of the solutions of the heat equations with absorption on networks. J Math Anal Appl, 2011, 380(2):642-652 [5] Dodziuk J, Kendall W S. Combinatorial Laplacians and the isoperimetric inequality//Ellworthy K D. From Local Times to Global Geometry. Control and Physics. Pitman Research Notes in Mathematics Series 150. Essex:Longman Scientific and Technical, 1986:68-74 [6] Fujita H. On the blowing up of solutions of the Cauchy problem for ut=△u+u1+α. J Fac Sci Univ Tokyo Sect A Math, 1966, 13(2):109-124 [7] Fujita H. On some nonexistence and nonuniqueness theorems for nonlinear parabolic equations. Symp Pure Mathematics, 1969, 18:105-113 [8] Grigor'yan A. Analysis on Graphs. University Bielefeld, 2009 [9] Grigor'yan A, Lin Y, Yang Y. Yamabe type equations on graphs. J Differential Equations, 2016, 261(9):4924-4943 [10] Grigor'yan A, Lin Y, Yang Y. Kazdan-Warner equation on graph. Calc Var Partial Differential Equations, 2016, 55(4):92(13 pages) [11] Grigor'yan A, Lin Y, Yang Y. Existence of positive solutions to some nonlinear equations on locally finite graphs. Sci China Math, 2017, 60(7):1311-1324 [12] Haeseler S, Keller M, Lenz D, Wojciechowski R. Laplacians on infinite graphs:Dirichlet and Neumann boundary conditions. J Spectr Theory, 2012, 2(4):397-432 [13] Kaplan S. On the growth of solutions of quasilinear parabolic equations. Comm Pure Appl Math, 1963, 16:305-333 [14] Lin Y, Wu Y. On-diagonal lower estimate of heat kernels on graphs. J Math Anal Appl, 2017, 456:1040-1048 [15] Lin Y, Wu Y. The existence and nonexistence of global solutions for a semilinear heat equation on graphs. Calc Var Partial Differential Equations, 2017, 56(4):102(22 pages) [16] Liu W, Chen K, Yu J. Extinction and asymptotic behavior of solutions for the ω-heat equation on graphs with source and interior absorption. J Math Anal Appl, 2016, 435(1):112-132 [17] Osgood W F. Beweis der Existenz einer Lösung der Differentialgleichung dy/dx=f(x, y) ohne Hinzunahme der Cauchy-Lipschitzschen Bedingung. Monatshefte der Mathemratik unid Physik, 1898, 9(1):331-345 [18] Weber A. Analysis of the physical Laplacian and the heat flow on a locally finite graph. J Math Anal Appl, 2012, 370(1):146-158 [19] Wojciechowski R. Heat kernel and essential spectrum of infinite graphs. Indiana Univ Math J, 2008, 58(3):1419-1442 [20] Xin Q, Xu L, Mu C. Blow-up for the ω-heat equation with Dirichelet boundary conditions and a reaction term on graphs. Appl Anal, 2014, 93(8):1691-1701 |