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January  2009, 8(1): 179-193. doi: 10.3934/cpaa.2009.8.179

On the asymptotic behavior of elliptic, anisotropic singular perturbations problems

Michel Chipot 1, and  Senoussi Guesmia 2,

1. 

University of Zürich, Institute of Mathematics, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
2. 

University of Zürich, Institute of Mathematics, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland

Received  June 2008 Revised  August 2008 Published  October 2008

In this paper, we consider anitropic singular perturbations of some elliptic boundary value problems. We study the asymptotic behavior as $\varepsilon \rightarrow 0$ for the solution. Strong convergence in some Sobolev spaces is proved and the rate of convergence in cylindrical domains is given.
Keywords: asymptotic behavior, Anisotropic singular perturbations, elliptic problems..
Mathematics Subject Classification: Primary: 35B25, 35B40; Secondary: 35J2.
Citation: Michel Chipot, Senoussi Guesmia. On the asymptotic behavior of elliptic, anisotropic singular perturbations problems. Communications on Pure & Applied Analysis, 2009, 8 (1) : 179-193. doi: 10.3934/cpaa.2009.8.179
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