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Approximation ofa semilinear elliptic problem in an unbounded domain

Published online by Cambridge University Press:  15 March 2003

Messaoud Kolli  and
Michelle Schatzman
Messaoud Kolli
Affiliation:
Département de Mathématiques, Université Ferhat-Abbas, Sétif 19000, Algérie. kollimes@yahoo.fr.
Michelle Schatzman
Affiliation:
MAPLY, CNRS, Université Claude Bernard – Lyon 1, 21 Avenue Claude Bernard, 69622 Villeurbanne Cedex, France. schatz@maply.univ-lyon1.fr.
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Abstract

Let f be an odd function of a class C2 such that ƒ(1) = 0,ƒ'(0) < 0,ƒ'(1) > 0 and $x\mapsto f(x)/x$ increases on [0,1]. We approximate the positive solution of Δu + ƒ(u) = 0, on $ \xR_{+}^{2}$ with homogeneous Dirichlet boundary conditions by the solution of $-\Delta u_{L}+f(u_{L})=0,$ on ]0,L[2 with adequate non-homogeneous Dirichlet conditions. We show that the error uL - u tends to zero exponentially fast, in the uniform norm.

Keywords

Semilinear elliptic equationsfull-space problemsapproximation by finite domains.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 1 , January 2003 , pp. 117 - 132
Copyright
© EDP Sciences, SMAI, 2003

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