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Optimal control of a parabolic equation with a nonlocal nonlinearity.
- Source :
-
Journal of Differential Equations . Jan2024, Vol. 378, p234-263. 30p. - Publication Year :
- 2024
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *INTEGRAL domains
*EQUATIONS
*NONLINEAR equations
*ADJOINT differential equations
Subjects
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 378
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 173472715
- Full Text :
- https://doi.org/10.1016/j.jde.2023.09.025