Blow-up for a semilinear heat equation with Fujita's critical exponent on locally finite graphs

DOI10.1007/S13398-021-01075-7zbMath1472.35068arXiv2004.07596OpenAlexW3171651521MaRDI QIDQ2050200

Yiting Wu

Publication date: 30 August 2021

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.07596

zbMATH Keywords

blow-upcritical exponentheat kernel estimate on graphssemilinear heat equation on graphs

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Blow-up in context of PDEs (35B44) Semilinear parabolic equations (35K58) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

Related Items (11)

BLOW-UP PROBLEMS FOR GENERALIZED FUJITA-TYPE EQUATIONS ON GRAPHS ⋮ The generalized porous medium equation on graphs: existence and uniqueness of solutions with \(\ell^1\) data ⋮ LOCAL EXISTENCE AND BLOW-UP OF SOLUTIONS TO FUJITA-TYPE EQUATIONS INVOLVING GENERAL ABSORPTION TERM ON FINITE GRAPHS ⋮ Blow-up of nonnegative solutions of an abstract semilinear heat equation with convex source ⋮ Nonexistence of global solutions for a class of nonlinear parabolic equations on graphs ⋮ A heat flow with sign-changing prescribed function on finite graphs ⋮ BLOW-UP PROBLEMS FOR FUJITA-TYPE PARABOLIC SYSTEM INVOLVING TIME-DEPENDENT COEFFICIENTS ON GRAPHS ⋮ Blow-up conditions for a semilinear parabolic system on locally finite graphs ⋮ Existence of solutions to the nonlinear Schrödinger equation on locally finite graphs ⋮ Unnamed Item ⋮ The existence of extremal functions for discrete Sobolev inequalities on lattice graphs

Cites Work

• Unnamed Item
• Unnamed Item
• Local monotonicity for the Yang-Mills-Higgs flow
• Hölder regularity of quasiminimizers under generalized growth conditions
• Yamabe equations on infinite graphs
• Yamabe type equations on graphs
• A logarithmic Sobolev form of the Li-Yau parabolic inequality
• Analysis of the physical Laplacian and the heat flow on a locally finite graph
• Existence and non-existence of global solutions for a semilinear heat equation
• On the growing problem for semilinear heat equations
• Existence of positive solutions to some nonlinear equations on locally finite graphs
• On nonexistence of global solutions for a semilinear heat equation on graphs
• Convergence of ground state solutions for nonlinear Schrödinger equations on graphs
• Laplacians on infinite graphs: Dirichlet and Neumann boundary conditions
• General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski problem. II
• Existence and convergence of solutions for nonlinear biharmonic equations on graphs
• Blow-up problems for nonlinear parabolic equations on locally finite graphs
• On-diagonal lower estimate of heat kernels for locally finite graphs and its application to the semilinear heat equations
• Li-Yau inequality on graphs
• Kazdan-Warner equation on graph in the negative case
• Dirichlet forms and stochastic completeness of graphs and subgraphs
• A note on Liouville type equations on graphs
• Kazdan-Warner equation on infinite graphs
• On nonexistence of global solutions of some semilinear parabolic differential equations
• MONOTONICITY AND ASYMPTOTIC PROPERTIES OF SOLUTIONS FOR PARABOLIC EQUATIONS VIA A GIVEN INITIAL VALUE CONDITION ON GRAPHS
• ON A CLASS OF NONLINEAR SCHRÖDINGER EQUATIONS ON FINITE GRAPHS
• The pth Kazdan–Warner equation on graphs
• On a class of quasilinear elliptic equation with indefinite weights on graphs
• Heat kernel and essential spectrum of infinite graphs

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