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Homogenization limit for the Diffusion Equation in a domain Perforated along (n - 1)-Dimensional Manifold with Dynamic Conditions on the Boundary of the Perforations: Critical Case
- Authors: Zubova M.N.1, Shaposhnikova T.A.1
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Affiliations:
- Lomonosov Moscow State University
- Issue: Vol 486, No 1 (2019)
- Pages: 12-19
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/13017
- DOI: https://doi.org/10.31857/S0869-5652486112-19
- ID: 13017
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Abstract
The problem of homogenization the diffusion equation in a domain perforated along an (n - 1)-dimensional manifold with dynamic boundary conditions on the boundary of the perforations is studied. A homogenization model is constructed that is a transmission problem for the diffusion equation with the transmission conditions containing a term with memory. A theorem on the convergence of solutions of the original problem to the solution of the homogenized one is proved.
About the authors
M. N. Zubova
Lomonosov Moscow State University
Email: shaposh.tan@mail.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991
T. A. Shaposhnikova
Lomonosov Moscow State University
Author for correspondence.
Email: shaposh.tan@mail.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991
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