The blow-up theorem of a discrete semilinear wave equation
Abstract
In this paper, the discretization of a nonlinear wave equation whose nonlinear term is a power function is introduced. The difference equation derived by discretizing the nonlinear wave equation has solutions which show characteristics corresponding to the characteristics of the blow-up solutions for the original equation. The initial value 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 value problem for the introduced difference equation, the introduced 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.1107.1917,
title = {The blow-up theorem of a discrete semilinear wave equation},
author = {Keisuke Matsuya},
journal= {arXiv preprint arXiv:1107.1917},
year = {2011}
}
Comments
9 pages