Homogenization of the heat equation in a noncylindrical domain with randomly oscillating boundary

Abstract

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 ε → 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.