Issue |
ESAIM: M2AN
Volume 33, Number 5, September October 1999
|
|
---|---|---|
Page(s) | 1057 - 1070 | |
DOI | https://doi.org/10.1051/m2an:1999134 | |
Published online | 15 August 2002 |
Homogenization of a monotone problem in a domain with oscillating boundary
1
Université de Rouen, UPRES-A 6085, 76821 Mont Saint
Aignan Cedex, France.
2
Università degli Studi di Napoli Federico II,
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”,
via Mezzocannone n. 8, 80134 Napoli, Italy.
3
Università degli Studi di Napoli Federico II,
Dipartimento di Ingegneria Agraria e Agronomia del territorio,
via Università n. 100, 80055 Portici (NA), Italy.
Received:
3
July
1998
Revised:
4
February
1999
We study the asymptotic behaviour
of the following nonlinear problem:
in a domain Ωh of
whose boundary ∂Ωh
contains an oscillating part with respect to h
when 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 to
the oscillating boundary identifies
with a diffusion operator with respect to
xn coupled with an algebraic problem
for the limit fluxes.
Résumé
Nous étudions le comportement asymptotique du
problème non linéaire monotone
posé sur un ouvert
Ωh de
dont une partie de la frontière oscille
avec h lorsque h tend vers ∞.
Cette partie oscillante est constituée
d'un ensemble de cylindres d'axe Oxn
distribués avec la période h-1.
Nous démontrons que dans le domaine correspondant à la
partie oscillante, le problème limite couple un
problème de diffusion en xn et un problème
algébrique pour les flux limites.
Mathematics Subject Classification: 35B25 / 35J60
Key words: Homogenization / nonlinear problem / oscillating boundary.
© EDP Sciences, SMAI, 1999
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