Electron. J. Diff. Eqns., Vol. 2008(2008), No. 59, pp. 1-13.

Asymptotic behavior of elliptic boundary-value problems with some small coefficients

Senoussi Guesmia

The aim of this paper is to analyze the asymptotic behavior of the solutions to elliptic boundary-value problems where some coefficients become negligible on a cylindrical part of the domain. We show that the dimension of the space can be reduced and find estimates of the rate of convergence. Some applications to elliptic boundary-value problems on domains becoming unbounded are also considered.

Submitted November 16, 2007. Published April 18, 2008.
Math Subject Classifications: 35B25, 35B40, 35J25.
Key Words: Elliptic problem; singular perturbations; asymptotic behavior.

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Senoussi Guesmia
Service de Métrologie Nucleaire, Université Libre de Bruxelles
C. P. 165, 50, Av. F. D. Roosevelt, B-1050 Brussels, Belgium.
Laboratoire Mathématiques, Informatique et Applications (MIA)
4, rue des Frères Lumière 68093 Mulhouse CEDEX France
email: senoussi.guesmia@uha.fr, sguesmia@ulb.ac.be

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