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
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.