| Attributs | Valeurs |
|---|
| type
| |
| Is Part Of
| |
| Subject
| |
| Title
| - Homogenization in perforated domains with rapidly pulsing perforations
|
| Date
| |
| has manifestation of work
| |
| related by
| |
| Author
| |
| Abstract
| - The aim of this paper is to study a class of domains whose geometry strongly depends on time namely. More precisely, we consider parabolic equations in perforated domains with rapidly pulsing (in time) periodic perforations, with a homogeneous Neumann condition on the boundary of the holes. We study the asymptotic behavior of the solutions as the period ε of the holes goes to zero. Since standard conservation laws do not hold in this model, a first difficulty is to get a priori estimates of the solutions. We obtain them in a weighted space where the weight is the principal eigenfunction of an “adjoint” periodic time-dependent eigenvalue problem. This problem is not a classical one, and its investigation is an important part of this work. Then, by using the multiple scale method, we construct the leading terms of a formal expansion (with respect to ε) of the solution and give the limit “homogenized” problem. An interesting peculiarity of the model is that, depending on the geometry of the holes, a large convection term may appear in the limit equation.
|
| article type
| |
| publisher identifier
| |
| Date Copyrighted
| |
| Rights
| - © EDP Sciences, SMAI, 2003
|
| Rights Holder
| |
| is part of this journal
| |
| is primary topic
of | |
