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

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Abstract

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.

About the authors

A. V. Podolskiy

Lomonosov Moscow State University

Author for correspondence.
Email: AVPodolskiy@yandex.ru
Moscow, Russia

T. A. Shaposhnikova

Lomonosov Moscow State University

Email: shaposh.tan@mail.ru
Moscow, Russia

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Copyright (c) 2022 Podolskiy A.V., Shaposhnikova T.A.

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