# American Institute of Mathematical Sciences

March  2020, 19(3): 1669-1695. doi: 10.3934/cpaa.2020061

## Homogenization of a locally periodic time-dependent domain

 Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran

* Corresponding author

Received  February 2019 Revised  August 2019 Published  November 2019

We consider the homogenization of a Robin boundary value problem in a locally periodic perforated domain which is also time-dependent. We aim at justifying the homogenization limit, that we derive through asymptotic expansion technique. More exactly, we obtain the so-called corrector homogenization estimate that specifies the convergence rate. The major challenge is that the media is not cylindrical and changes over time. We also show the existence and uniqueness of solutions of the microscopic problem.

Citation: Morteza Fotouhi, Mohsen Yousefnezhad. Homogenization of a locally periodic time-dependent domain. Communications on Pure & Applied Analysis, 2020, 19 (3) : 1669-1695. doi: 10.3934/cpaa.2020061
##### References:

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##### References:
Schematic representation of a locally periodic heterogeneous medium in a time slice
Schematic a non-cylindrical domain approximated by a family of cylindrical domains
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