Volume 30, pp. 237-246, 2008.

Asymptotic behavior for numerical solutions of a semilinear parabolic equation with a nonlinear boundary condition

Nabongo Diabate and Théodore K. Boni

Abstract

This paper concerns the study of the numerical approximation for the following initial-boundary value problem, ut=uxxaup,0<x<1,t>0,ux(0,t)=0,ux(1,t)+buq(1,t)=0,t>0,u(x,0)=u0(x)0,0x1, where a>0, b>0 and p>q>1. We show that the solution of a semidiscrete form of the initial value problem above goes to zero as t approaches infinity and give its asymptotic behavior. We provide some numerical experiments that illustrate our analysis.

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Key words

semidiscretizations, semilinear parabolic equation, asymptotic behavior, convergence

AMS subject classifications

35B40, 35B50, 35K60, 65M06