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

Abstract

We study the asymptotic behaviour of a linear optimal control problem posed on a locally periodic rapidly oscillating domain. We consider an $L^2$-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.

Keywords:

• Homogenization
• asymptotic analysis
• periodic unfolding
• locally periodic boundary
• optimal control

2000 Mathematics Subject Classifications:

• 80M35
• 80M40
• 35B27

Acknowledgements

The research by G.C. and C.P was supported by project GNAMPA (INDAM) 2023 “Analisi asintotica di problemi al contorno in strutture sottili o rugose”.

Disclosure statement

No potential conflict of interest was reported by the author(s).