BLOW-UP PROBLEMS FOR NONLINEAR PARABOLIC EQUATIONS ON LOCALLY FINITE GRAPHS

doi:10.1016/S0252-9602(18)30788-4

Abstract

Abstract:

Let G=(V, E) be a locally finite connected weighted graph, and △ be the usual graph Laplacian. In this article, we study blow-up problems for the nonlinear parabolic equation u_t=△u + f(u) on G. The blow-up phenomenons for u_t=△u + f(u) 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 corresponding solutions will blow up in a finite time.

Key words: Blow-up, parabolic equations, locally finite graphs, differential inequalities

Yong LIN, Yiting WU. BLOW-UP PROBLEMS FOR NONLINEAR PARABOLIC EQUATIONS ON LOCALLY FINITE GRAPHS[J].Acta mathematica scientia,Series B, 2018, 38(3): 843-856.

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