Approximation of a semilinear elliptic problem in an unbounded domain
Département de Mathématiques, Université Ferhat-Abbas,
Sétif 19000, Algérie. email@example.com.
2 MAPLY, CNRS, Université Claude Bernard – Lyon 1, 21 Avenue Claude Bernard, 69622 Villeurbanne Cedex, France. firstname.lastname@example.org.
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