Homogenization of a locally periodic time-dependent domain

Morteza Fotouhi; Mohsen Yousefnezhad

doi:10.3934/cpaa.2020061

Homogenization of a locally periodic time-dependent domain

Morteza Fotouhi, Mohsen Yousefnezhad

Research output: Journal Publication › Article › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1669-1695
Number of pages	27
Journal	Communications on Pure and Applied Analysis
Volume	19
Issue number	3
DOIs	https://doi.org/10.3934/cpaa.2020061
Publication status	Published - 2020
Externally published	Yes

Keywords

Corrector estimates
Homogenization limit
Locally periodic microstructure
Time-dependent domain

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.3934/cpaa.2020061

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title = "Homogenization of a locally periodic time-dependent domain",

abstract = "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.",

keywords = "Corrector estimates, Homogenization limit, Locally periodic microstructure, Time-dependent domain",

author = "Morteza Fotouhi and Mohsen Yousefnezhad",

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T1 - Homogenization of a locally periodic time-dependent domain

AU - Fotouhi, Morteza

AU - Yousefnezhad, Mohsen

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Corrector estimates

KW - Homogenization limit

KW - Locally periodic microstructure

KW - Time-dependent domain

UR - https://www.scopus.com/pages/publications/85075628209

U2 - 10.3934/cpaa.2020061

DO - 10.3934/cpaa.2020061

M3 - Article

AN - SCOPUS:85075628209

SN - 1534-0392

VL - 19

SP - 1669

EP - 1695

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 3

ER -

Homogenization of a locally periodic time-dependent domain

Abstract

Keywords

ASJC Scopus subject areas

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