Journal
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Volume 45, Issue 10, Pages 6435-6458Publisher
WILEY
DOI: 10.1002/mma.8179
Keywords
evolving boundary; homogenization; parabolic equations; random oscillating boundary
Categories
Funding
- University Grants Commission [F.4-2/2006 (BSR)/MA/19-20/0060]
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This article studies the homogenization of heat equations in a domain with randomly oscillating boundary parts. A new homogenization technique is utilized to deal with the evolving domains, and a corrector result is established.
In this article, we study the homogenization of heat equations in a domain with randomly oscillating boundary parts. The random oscillating boundary is time-dependent and confined by a stationary random field. Here, we follow a new homogenization technique that deals with the evolving domains, which covers many applications. We obtain the asymptotic limit as epsilon -> 0 in the reference configuration, in which the heat equation becomes a parabolic equation with random oscillating coefficients in the reference domain. To the best of our knowledge, this is the first result of the homogenization of problems on the random evolving boundary domain. One of the major contributions is the corrector result which we establish in this article.
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