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Asymptotic behavior of the numerical solutions of time-delayed reaction diffusion equations with non-monotone reaction term

Published online by Cambridge University Press:  15 November 2003

Yuan-Ming Wang
Yuan-Ming Wang*
Affiliation:
Department of Mathematics, East China Normal University, Shanghai 200062, China. ymwang@math.ecnu.edu.cn.
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Abstract

This paper is concerned with the asymptotic behavior of the finite difference solutions of a class of nonlinear reaction diffusion equations with time delay. By introducing a pair of coupled upper and lower solutions, an existence result of the solution is given and an attractor of the solution is obtained without monotonicity assumptions on the nonlinear reaction function. This attractor is a sector between two coupled quasi-solutions of the corresponding “steady-state" problem, which are obtained from a monotone iteration process. A sufficient condition, ensuring that two coupled quasi-solutions coincide, is given. Also given is the application to a nonlinear reaction diffusion problem with time delay for three different types of reaction functions, including some numerical results which validate the theoretical analysis.

Keywords

Asymptotic behaviorfinite difference equationreaction diffusion equationtime delayupper and lower solutions.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 2 , March 2003 , pp. 259 - 276
Copyright
© EDP Sciences, SMAI, 2003

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