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

2020/04/16 by Wu, Yiting · 2 citations
#35A01 #35K91 #35R02 #58J35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2004.07596

Abstract

Let G=(V,E) be a locally finite, connected and weighted graph. We prove that, for a graph satisfying curvature dimension condition CDE'(n,0) and uniform polynomial volume growth of degree m, all non-negative solutions of the equation ∂_tu=Δu+u^1+α blow up in a finite time provided that α=(2)/(m). We also consider the blow-up problem under certain conditions for volume growth and initial value. The obtained results provide a significant complement to the work by Lin and Wu in earlier paper.

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• Blow up results and lifespan estimates for nonlinear damped wave equations on weighted graphs
• Blow-up solutions of parabolic p-Laplacian inequalities on locally finite graphs

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