Blow-up of solutions to a Dirichlet problem for the discrete semi-linear heat equation
Abstract
In this paper, the initial and boundary problem of the difference equation which is a discretization of the semi-linear heat equation. The difference equation derived by discretizing the semi-linear heat equation has solutions which show characteristics corresponding to the characteristics of the blow-up solutions for the original equation. The initial and boundary problem for the original equation has blow-up solutions when a certain condition is met. We prove that when a similar condition as that of the original solution is met in the initial and boundary problem for the difference equation, the difference equation has blow-up solutions having characteristics corresponding to the characteristics of the blow-up solutions for the original equation.
Keywords
Cite
@article{arxiv.1211.1192,
title = {Blow-up of solutions to a Dirichlet problem for the discrete semi-linear heat equation},
author = {Keisuke Matsuya},
journal= {arXiv preprint arXiv:1211.1192},
year = {2012}
}