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Homogenization of a class of quasilinear elliptic equations in high-contrast fissured media

Published online by Cambridge University Press:  12 July 2007

B. Amaziane ,
L. Pankratov  and
A. Piatnitski
B. Amaziane
Affiliation:
Laboratoire de Mathématiques Appliquées, CNRS-UMR5142, Université de Pau, Av. de l'Université, 64000 Pau, France ([email protected])
L. Pankratov
Affiliation:
Laboratoire de Mathématiques Appliquées, CNRS-UMR5142, Université de Pau, Av. de l'Université, 64000 Pau, France
A. Piatnitski
Affiliation:
Narvik University College, Postbox 385, Narvik 8505, Norway and Lebedev Physical Institute, Russian Academy of Sciences, Leninskii pr. 53, Moscow 119991, Russia ([email protected])
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Abstract

The aim of the paper is to study the asymptotic behaviour of the solution of a quasilinear elliptic equation of the form with a high-contrast discontinuous coefficient aε(x), where ε is the parameter characterizing the scale of the microstucture. The coefficient aε(x) is assumed to degenerate everywhere in the domain Ω except in a thin connected microstructure of asymptotically small measure. It is shown that the asymptotical behaviour of the solution uε as ε → 0 is described by a homogenized quasilinear equation with the coefficients calculated by local energetic characteristics of the domain Ω.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 6 , December 2006 , pp. 1131 - 1155
Copyright
Copyright © Royal Society of Edinburgh 2006

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