Homogenization of a Parabolic Equation in a Perforated Domain with a Unilateral Dynamic Boundary Condition: Critical Case

The present paper studies the homogenization of the parabolic equation stated 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 t...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 283; no. 1; pp. 111 - 124
Main Authors Podolskiy, A. V., Shaposhnikova, T. A.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 2024
Springer Nature B.V
Subjects
Boundary conditions
Differential equations
Homogenization
Mathematics
Mathematics and Statistics
Operators (mathematics)
perforated domain
critical case
strange nonlocal term
homogenization of parabolic equation
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Summary:The present paper studies the homogenization of the parabolic equation stated 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 to the variational problem involving an ordinary differential operator.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-024-07242-6