# Approximation of a semilinear elliptic problem in an unbounded domain

Messaoud Kolli; Michelle Schatzman

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- 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 37.1 (2010): 117-132. <http://eudml.org/doc/194148>.

@article{Kolli2010,

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.
},

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

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

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

language = {eng},

month = {3},

number = {1},

pages = {117-132},

publisher = {EDP Sciences},

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

url = {http://eudml.org/doc/194148},

volume = {37},

year = {2010},

}

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

DA - 2010/3//

PB - EDP Sciences

VL - 37

IS - 1

SP - 117

EP - 132

AB -
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.

LA - eng

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

UR - http://eudml.org/doc/194148

ER -

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