Homogenization of an optimal control problem in a domain with highly oscillating boundary using periodic unfolding method

Abstract

The method of unfolding is used to study optimal control problem in a domain with oscillating boundary. We consider Neumann condition on the oscillating part of the boundary and the result is more interesting than the Dirichlet condition. Here the limit problem consists of two parts, namely in the lower part and upper part with appropriate interface conditions. In this article, we have considered two cost functionals, namely $L^2$ and Dirichlet cost functionals. Interior and boundary unfolding operators are introduced in the process.