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Homogenization of a monotone problemin a domain with oscillating boundary

Published online by Cambridge University Press:  15 August 2002

Dominique Blanchard ,
Luciano Carbone  and
Antonio Gaudiello
Dominique Blanchard
Affiliation:
Université de Rouen, UPRES-A 6085, 76821 Mont Saint Aignan Cedex, France.
Luciano Carbone
Affiliation:
Università degli Studi di Napoli Federico II, Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, via Mezzocannone n. 8, 80134 Napoli, Italy.
Antonio Gaudiello
Affiliation:
Università degli Studi di Napoli Federico II, Dipartimento di Ingegneria Agraria e Agronomia del territorio, via Università n. 100, 80055 Portici (NA), Italy.
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Abstract

We study the asymptotic behaviour of the following nonlinear problem: $$\{\begin{array}{ll}-{\rm div}(a( Du_h))+\vert u_h\vert^{p-2}u_h =f \quad\hbox{in }\Omega_h, a( Du_h)\cdot\nu = 0 \quad\hbox{on }\partial\Omega_h, \end{array}.$$

in a domain Ωh of $\mathbb{R}^n$ whose boundary ∂Ωh contains an oscillating part with respect to hwhen h tends to ∞. The oscillating boundary is defined by a set of cylinders with axis 0xn that are h -1-periodically distributed. We prove that the limit problem in the domain corresponding tothe oscillating boundary identifieswith a diffusion operator with respect tox n coupled with an algebraic problemfor the limit fluxes.

Keywords

Homogenizationnonlinear problemoscillatingboundary.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 5 , September 1999 , pp. 1057 - 1070
Copyright
© EDP Sciences, SMAI, 1999

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