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

Abstract

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Let f be an odd function of a class C2 such that ƒ(1) = 0,ƒ'(0) < 0,ƒ'(1) > 0 and x ↦ f ( x ) / x increases on [0,1]. We approximate the positive solution of Δu + ƒ(u) = 0, on + 2 with homogeneous Dirichlet boundary conditions by the solution of - Δ 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.

How to cite

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Kolli, 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 -

References

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