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

Yong Lin; Yiting Wu

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

Analysis of PDEs 2017-04-20 v1

Authors: Yong Lin , Yiting Wu

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.

Keywords

blow-up problems nonlinear parabolic equations locally finite graphs graph Laplacian Dirichlet boundary condition finite time blow-up

Cite

@article{arxiv.1704.05702,
  title  = {Blow-up problems for nonlinear parabolic equations on locally finite graphs},
  author = {Yong Lin and Yiting Wu},
  journal= {arXiv preprint arXiv:1704.05702},
  year   = {2017}
}

Comments

14 pages

Related papers

View all related →