PARABOLIC PROBLEMS WITH DYNAMICAL BOUNDARY CONDITIONS IN PERFORATED MEDIA
Claudia Timofte · Mathematical Modelling and Analysis · 2003
The asymptotic behavior of the solution of a parabolic dynamical boundary‐value problem in a periodically perforated domain is analyzed. The perforations, which are identical and periodically distributed, are of size ϵ. In the perforated domain we consider a heat equation, with a Dirichlet condition on the exterior boundary and a dynamical boundary condition on the surface of the holes. The limit equation, as ϵ ? 0, is a heat equation with extra-terms coming from the influence of the non-homogeneous dynamical boundary condition.