Issue |
ESAIM: M2AN
Volume 37, Number 1, January/February 2003
|
|
---|---|---|
Page(s) | 117 - 132 | |
DOI | https://doi.org/10.1051/m2an:2003017 | |
Published online | 15 March 2003 |
Approximation of a semilinear elliptic problem in an unbounded domain
1
Département de Mathématiques, Université Ferhat-Abbas,
Sétif 19000, Algérie. kollimes@yahoo.fr.
2
MAPLY,
CNRS, Université Claude Bernard – Lyon 1, 21 Avenue Claude Bernard,
69622 Villeurbanne Cedex, France. schatz@maply.univ-lyon1.fr.
Received:
30
August
2001
Revised:
30
September
2002
Let f be an odd function of a class C2 such that ƒ(1) = 0,ƒ'(0) < 0,ƒ'(1) > 0 and increases on
[0,1]. We approximate the positive solution of Δu + ƒ(u) = 0, on
with homogeneous Dirichlet boundary conditions by the
solution of
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.
Mathematics Subject Classification: 35J60 / 35P15
Key words: Semilinear elliptic equations / full-space problems / approximation by finite domains.
© EDP Sciences, SMAI, 2003
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