Homogenization of variational functionals with nonstandard growth in perforated domains

Brahim Amaziane; Leonid Pankratov; Andrey Piatnitski

doi:10.3934/nhm.2010.5.189

Article Contents

2010, Volume 5, Issue 2: 189-215. Doi: 10.3934/nhm.2010.5.189

This issue Previous Article Next Article A mathematical model for dynamic wettability alteration controlled by water-rock chemistry

Homogenization of variational functionals with nonstandard growth in perforated domains

1.
Laboratoire de Mathématiques et de leurs Applications, CNRS-UMR 5142, Université de Pau, Av. de l’Université, 64000 Pau
2.
Department of Mathematics, B.Verkin Institute for Low Temperature Physics and Engineering, 47, av. Lenin, 61103, Kharkov
3.
Narvik University College, Postbox 385, Narvik, 8505

Received: October 31, 2009

Revised: January 31, 2010

Published: May 2010

Abstract Related Papers Cited by

Abstract

The aim of the paper is to study the asymptotic behavior of solutions to a Neumann boundary value problem for a nonlinear elliptic equation with nonstandard growth condition of the form

-div(|$\nabla$ u^ε | ^p_ε(x)-2 $\nabla$ u^ε )+ (| u^ε | ^p_ε(x)-2 u^ε= f(x)

in a perforated domain Ω^ε , ε being a small parameter that characterizes the microscopic length scale of the microstructure. Under the assumption that the functions p_ε(x) converge uniformly to a limit function $p_0(x)$ and that $p_0$ satisfy certain logarithmic uniform continuity condition, it is shown that u^ε converges, as ε$ \to 0$, to a solution of homogenized equation whose coefficients are calculated in terms of local energy characteristics of the domain Ω^ε. This result is then illustrated with periodic and locally periodic examples.

Keywords:

Mathematics Subject Classification: Primary: 35B40; 35J60; 46E35; Secondary: 74Q05; 76M50.

Citation:

Article Metrics

HTML views() PDF downloads(61) Cited by(0)

Homogenization of variational functionals with nonstandard growth in perforated domains

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Homogenization of variational functionals with nonstandard growth in perforated domains

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content