Optimal control of a parabolic equation with a nonlocal nonlinearity
Optimization and Control
2024-03-20 v1 Analysis of PDEs
Abstract
This paper proposes an optimal control problem for a parabolic equation with a nonlocal nonlinearity. The system is described by a parabolic equation involving a nonlinear term that depends on the solution and its integral over the domain. We prove the existence and uniqueness of the solution to the system and the boundedness of the solution. Regularity results for the control-to-state operator, the cost functional and the adjoint state are also proved. We show the existence of optimal solutions and derive first-order necessary optimality conditions. In addition, second-order necessary and sufficient conditions for optimality are established.
Keywords
Cite
@article{arxiv.2306.14559,
title = {Optimal control of a parabolic equation with a nonlocal nonlinearity},
author = {Cyrille Kenne and Landry Djomegne and Gisèle Mophou},
journal= {arXiv preprint arXiv:2306.14559},
year = {2024}
}