Optimal Control Problems of a Class of Nonlinear Degenerate Parabolic Equations

Yang Na, Tianjiao Men, Runmei Du () and Yingjie Zhu
Additional contact information
Yang Na: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
Tianjiao Men: School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China
Runmei Du: School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China
Yingjie Zhu: School of Mathematics and Statistics, Changchun University, Changchun 130012, China

Mathematics, 2024, vol. 12, issue 14, 1-19

Abstract: The optimal control problems of degenerate parabolic equations have many applications in economics, physics, climatology, and so on. Motivated by the applications, we consider the optimal control problems of a class of nonlinear degenerate parabolic equations in this paper. The main result is that we deduce the first order necessary condition for the optimal control problem of nonlinear degenerate parabolic equations by variation method. Moreover, we investigate the uniqueness of the solutions to the optimal control problems. For the linear equations, we obtain the global uniqueness, while for the nonlinear equations, we obtain only the local uniqueness. Finally, we give a numerical example to validate the theoretical results.

Keywords: the optimal control; degenerate parabolic equations; the first order necessary conditions; nonlinear equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/14/2181/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/14/2181/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:14:p:2181-:d:1433555

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().