Approximation of a semilinear elliptic problem in an unbounded domain

Kolli, Messaoud ; Schatzman, Michelle

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 37 (2003), p. 117-132 / Harvested from Numdam

Résumé

Let $f$ be an odd function of a class $\mathrm {C}^{2}$ such that $f(1)=0,f^{\prime }(0)<0,f^{\prime }(1)>0$ and $x\mapsto f(x)/x$ increases on $[0,1]$. We approximate the positive solution of $-\Delta u+f(u)=0,$ on $\mathbb {R}_{+}^{2}$ 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 $u_{L}-u$ tends to zero exponentially fast, in the uniform norm.

Détail

Publié le : 2003-01-01

MR 1972653 | Zbl 1137.35364

DOI : https://doi.org/10.1051/m2an:2003017
Classification:  35J60,  35P15

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