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ΓD-convergence for a class of quasilinear elliptic equations in thin structures

✍ Scribed by B. Amaziane; M. Goncharenko; L. Pankratov

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
169 KB
Volume
28
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

We study the asymptotic behaviour of the solution of a stationary quasilinear elliptic problem posed in a domain Ω^(ε)^ of asymptotically degenerating measure, i.e. meas Ω^(ε)^ → 0 as ε → 0, where ε is the parameter that characterizes the scale of the microstructure. We obtain the convergence of the solution and the homogenized model of the problem is constructed using the notion of convergence in domains of degenerating measure. Proofs are given using the method of local characteristics of the medium Ω^(ε)^ associated with our problem in a variational form. Copyright © 2005 John Wiley & Sons, Ltd.

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