Minimization of the Compliance under a Nonlocal p -Laplacian Constraint

Fuensanta Andrés, Damián Castaño () and Julio Muñoz
Additional contact information
Fuensanta Andrés: Departamento de Matemáticas, Universidad de Castilla-La Mancha, Avda. Carlos III s/n, 45071 Toledo, Spain
Damián Castaño: Departamento de Matemáticas, Universidad de Castilla-La Mancha, Avda. Carlos III s/n, 45071 Toledo, Spain
Julio Muñoz: Departamento de Matemáticas, Universidad de Castilla-La Mancha, Avda. Carlos III s/n, 45071 Toledo, Spain

Mathematics, 2023, vol. 11, issue 7, 1-22

Abstract: This work is an extension of the paper by Cea and Malanowski to the nonlocal and nonlinear framework. The addressed topic is the study of an optimal control problem driven by a nonlocal p -Laplacian equation that includes a coefficient playing the role of control in the optimization problem. The cost functional is the compliance, and the constraint on the states are of the Dirichlet homogeneous type. The goal of the present work is a numerical scheme for the nonlocal optimal control problem and its use to approximate solutions in the local setting. The main contributions of the paper are a maximum principle and a uniqueness result. These findings and the monotonicity properties of the p -Laplacian operator have been crucial to building an effective numerical scheme, which, at the same time, has provided the existence of optimal designs. Several numerical simulations complete the work.

Keywords: optimal control; non-local optimal control; approximation in optimal control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/7/1679/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/7/1679/ (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:11:y:2023:i:7:p:1679-:d:1112940

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 ().