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

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.