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Abstract 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… Click to show full abstract
Abstract 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.
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2018
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