Homogenization of a~parabolic equation in a~perforated domain with a~unilateral dynamic boundary condition: critical case

A. V. Podolskiy ; T. A. Shaposhnikova

Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 68 (2022) no. 4, pp. 671-685.

Résumé

In this paper, we study the homogenization of a parabolic equation given in a domain perforated by “tiny” balls. On the boundary of these perforations, a unilateral dynamic boundary constraints are specified. We address the so-called “critical” case that is characterized by a relation between the coefficient in the boundary condition, the period of the structure and the size of the holes. In this case, the homogenized equation contains a nonlocal “strange” term. This term is obtained as a solution of the variational problem involving ordinary differential operator.

Détail

Keywords: homogenization of parabolic equation, perforated domain, critical case
Mots-clés : strange nonlocal term.

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