# Approximation of a semilinear elliptic problem in an unbounded domain

Messaoud Kolli; Michelle Schatzman

- Volume: 37, Issue: 1, page 117-132
- ISSN: 0764-583X

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topKolli, Messaoud, and Schatzman, Michelle. "Approximation of a semilinear elliptic problem in an unbounded domain." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 37.1 (2003): 117-132. <http://eudml.org/doc/245741>.

@article{Kolli2003,

abstract = {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.},

author = {Kolli, Messaoud, Schatzman, Michelle},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {semilinear elliptic equations; full-space problems; approximation by finite domains},

language = {eng},

number = {1},

pages = {117-132},

publisher = {EDP-Sciences},

title = {Approximation of a semilinear elliptic problem in an unbounded domain},

url = {http://eudml.org/doc/245741},

volume = {37},

year = {2003},

}

TY - JOUR

AU - Kolli, Messaoud

AU - Schatzman, Michelle

TI - Approximation of a semilinear elliptic problem in an unbounded domain

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2003

PB - EDP-Sciences

VL - 37

IS - 1

SP - 117

EP - 132

AB - 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.

LA - eng

KW - semilinear elliptic equations; full-space problems; approximation by finite domains

UR - http://eudml.org/doc/245741

ER -

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