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Abstract
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.
Nagrinejamas parabolinis uždavinys su dinaminemis kraštinemis salygomis periodiškai perforuotoje srityje. Analizuojamos šio uždavinio sprendinio asimptotines savybes, kai mažas parametras yra perforacijos dydis, iš mikromodelio išvedamos matematinio makromodelio lygtys ir papildomosios salygos.