Optimal Control of Two-Phase Membrane Problem
Optimization and Control
2024-05-20 v1 Analysis of PDEs
Abstract
We consider an optimal control problem where the state is governed by a free boundary problem called the two-phase membrane problem and the control appears in the coefficients of the characteristic function of the positivity and negativity parts of the solution. Our investigation focuses on various properties associated with the control-to-state map. Due to the non-differentiability of this map, we regularize the state equation. The existence, uniqueness, and characterization of the optimal pairs are established.
Cite
@article{arxiv.2405.10704,
title = {Optimal Control of Two-Phase Membrane Problem},
author = {Farid Bozorgnia and Vyacheslav Kungurtsev},
journal= {arXiv preprint arXiv:2405.10704},
year = {2024}
}