Optimal control of a parabolic equation with a nonlocal nonlinearity - Archive ouverte HAL
Article Dans Une Revue Journal of Differential Equations Année : 2024

Optimal control of a parabolic equation with a nonlocal nonlinearity

Résumé

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

Dates et versions

hal-04581491 , version 1 (21-05-2024)

Identifiants

Citer

Cyrille Kenne, Landry Djomegne, Gisèle Mophou. Optimal control of a parabolic equation with a nonlocal nonlinearity. Journal of Differential Equations, 2024, 378, pp.234-263. ⟨10.1016/j.jde.2023.09.025⟩. ⟨hal-04581491⟩
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