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.
Paraboliniai uždaviniai su dinaminėmis kraštinėmis sąlygomis perforuotoje terpėje
Santrauka. Nagrinėjamas parabolinis uždavinys su dinaminėmis kraštinėmis sąlygomis periodiškai perforuotoje srityje. Analizuojamos šio uždavinio sprendinio asimptotinės savybės, kai mažas parametras yra perforacijos dydis, iš mikromodelio išvedamos matematinio makromodelio lygtys ir papildomosios sąlygos.
Timofte, C. (2003). Parabolic problems with dynamical boundary conditions in perforated media. Mathematical Modelling and Analysis, 8(4), 337-350. https://doi.org/10.3846/13926292.2003.9637235
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