Blow-up problems for nonlinear parabolic equations on locally finite graphs

Yong Lin; Yiting Wu

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arXiv · 1704.05702

Blow-up problems for nonlinear parabolic equations on locally finite graphs

Yong Lin·Yiting Wu

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Abstract

Let $G=(V,E)$ be a locally finite connected weighted graph, $\Delta$ be the usual graph Laplacian. In this paper, we study the blow-up problems for the nonlinear parabolic equation $u_t=\Delta u + f(u)$ on $G$. The blow-up phenomenons of the equation are discussed in terms of two cases: (i) an initial condition is given; (ii) a Dirichlet boundary condition is given. We prove that if $f$ satisfies appropriate conditions, then the solution of the equation blows up in a finite time.

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Yong Lin, Yiting Wu. 2017-04-19. Blow-up problems for nonlinear parabolic equations on locally finite graphs. https://arxiv.org/abs/1704.05702

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