Kolli, Messaoud; Schatzman, Michelle
Approximation of a semilinear elliptic problem in an unbounded domain
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 37 (2003) no. 1 , p. 117-132
Zbl 1137.35364 | MR 1972653
doi : 10.1051/m2an:2003017
URL stable : http://www.numdam.org/item?id=M2AN_2003__37_1_117_0

Classification:  35J60,  35P15
Let f be an odd function of a class C 2 such that f(1)=0,f ' (0)<0,f ' (1)>0 and xf(x)/x increases on [0,1]. We approximate the positive solution of -Δu+f(u)=0, on + 2 with homogeneous Dirichlet boundary conditions by the solution of -Δu 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.


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