Optimal control problem stated in a locally periodic rough domain: a homogenization study

We study the asymptotic behaviour of a linear optimal control problem posed on a locally periodic rapidly oscillating domain. We consider an L2-cost functional constrained by a Poisson problem having a mixed boundary condition: we assume a homogeneous Neumann condition on the oscillating part of the boundary and a homogeneous Dirichlet condition on the remaining part.

Automated summary

In this study, we examine the asymptotic behavior of a linear optimal control problem posed on a locally periodic rapidly oscillating domain. The problem involves an L2-cost functional constrained by a Poisson problem with a mixed boundary condition: a homogeneous Neumann condition on the oscillating part of the boundary and a homogeneous Dirichlet condition on the remaining part.