Approximation of a semilinear elliptic problem in an unbounded domain
ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 1, pp. 117-132.

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.

DOI : 10.1051/m2an:2003017
Classification : 35J60, 35P15
Mots clés : semilinear elliptic equations, full-space problems, approximation by finite domains
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     title = {Approximation of a semilinear elliptic problem in an unbounded domain},
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Kolli, Messaoud; Schatzman, Michelle. Approximation of a semilinear elliptic problem in an unbounded domain. ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 1, pp. 117-132. doi : 10.1051/m2an:2003017. http://www.numdam.org/articles/10.1051/m2an:2003017/

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