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Approximation of a semilinear elliptic problem in an unbounded domain

Messaoud KolliMichelle Schatzman — 2003

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

Let f be an odd function of a class C 2 such that f ( 1 ) = 0 , f ' ( 0 ) < 0 , f ' ( 1 ) > 0 and x f ( x ) / x increases on [ 0 , 1 ] . We approximate the positive solution of - Δ u + f ( 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 u L - u tends to zero exponentially fast, in the uniform norm.

Approximation of a semilinear elliptic problem in an unbounded domain

Messaoud KolliMichelle Schatzman — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

Let be an odd function of a class C such that ƒ(1) = 0,ƒ'(0) < 0,ƒ'(1) > 0 and x f ( x ) / x increases on . We approximate the positive solution of Δ = 0, on + 2 with homogeneous Dirichlet boundary conditions by the solution of - Δ u L + f ( u L ) = 0 , on ]0,[ with adequate non-homogeneous Dirichlet conditions. We show that the error tends to zero exponentially fast, in the uniform norm.

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