Optimal control problem for an anisotropic parabolic problem in a domain with very rough boundary

In this paper, using Pontryagin's maximum principle, we study the asymptotic behaviour of a parabolic optimal control problem in a domain whose boundary contains a highly oscillating part. On this part we consider a homogeneous Neumann boundary condition. We identify the limit problem, which is an optimal control problem for the limit equation. Moreover, we explicitly remark that both limit state equation and limit cost are different from those ones at epsilon-level