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Homogenization in perforated domains with rapidly pulsing perforations

Doina Cioranescu;  Andrey L. Piatnitski — 2003

ESAIM: Control, Optimisation and Calculus of Variations

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...

Homogenization in perforated domains with rapidly pulsing perforations

Doina Cioranescu;  Andrey L. Piatnitski — 2010

ESAIM: Control, Optimisation and Calculus of Variations

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 of the holes goes to zero. Since standard conservation laws do not hold in this model, a first difficulty is to get estimates of the solutions....

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