Nandakumaran, AK and Sankar, K (2022) Homogenization of the heat equation in a noncylindrical domain with randomly oscillating boundary. In: Mathematical Methods in the Applied Sciences .
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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. © 2022 John Wiley & Sons, Ltd.
| Item Type: | Journal Article |
|---|---|
| Publication: | Mathematical Methods in the Applied Sciences |
| Publisher: | John Wiley and Sons Ltd |
| Additional Information: | The copyright for this article belongs to John Wiley and Sons Ltd |
| Keywords: | Heat transfer; Homogenization method, Evolving boundary; Heat equation; Homogenization; Homogenization techniques; Noncylindrical domain; Oscillating boundaries; Parabolic Equations; Random oscillating boundary; Stationary random field; Time dependent, Partial differential equations |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 18 Mar 2022 11:58 |
| Last Modified: | 18 Mar 2022 11:58 |
| URI: | http://eprints.iisc.ac.in/id/eprint/71601 |
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