Homogenization of parabolic equation in an evolving domain with an oscillating boundary

被引:4
作者
Muthukumar, T. [1 ]
Raymond, Jean-Pierre [2 ,3 ]
Sankar, K. [1 ]
机构
[1] Indian Inst Technol, Kanpur 208016, Uttar Pradesh, India
[2] Univ Paul Sabatier, Inst Math Toulouse, F-31062 Toulouse, France
[3] CNRS, F-31062 Toulouse, France
关键词
Homogenization; Parabolic equations; Rough boundary; Evolving boundary; LAPLACE EQUATION; LAMINAR FLOWS; ROUGH; APPROXIMATION;
D O I
10.1016/j.jmaa.2018.03.063
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this article, we study the existence, uniqueness and homogenization of the heat equation in a domain with highly oscillating and evolving (time-dependent) boundary and an inhomogeneous time-dependent data on the oscillating part of boundary, motivated by fluid-structure interaction problems. We rewrite the parabolic equation in a reference configuration which transforms the boundary oscillations into rapidly oscillating coefficients. Finally, we obtain the effective coefficients and corrector results in the reference configuration. (C) 2018 Elsevier Inc. All rights reserved.
引用
收藏
页码:838 / 868
页数:31
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