Bilinear optimal control of a one‐dimensional degenerate parabolic equation with a nonlocal term-Reference-Cited by-同舟云学术

Bilinear optimal control of a one‐dimensional degenerate parabolic equation with a nonlocal term

Published:2024-04-24 Issue:14 Volume:47 Page:11670-11692
ISSN:0170-4214
Container-title:Mathematical Methods in the Applied Sciences
language:en
Short-container-title:Math Methods in App Sciences

Author:

Kenne Cyrille¹²^ORCID,Djomegne Landry³^ORCID,Larrouy James¹^ORCID

Affiliation:

1. LAMIA, Department of Mathematics Université des Antilles Pointe‐à‐Pitre Guadeloupe France

2. L3MA, UFR STE and IUT Université des Antilles Schoelcher Martinique France

3. University of Dschang Dschang Cameroon

Abstract

In this paper, a one‐dimensional degenerate parabolic equation involving a multiplicative control with a nonlocal space term represented by an integral kernel is considered. After some well‐posedness results, we derive several properties of the control‐to‐state mapping. We establish the existence of at least one optimal control and derive the first and the second conditions for optimality, giving the local uniqueness of an optimal control. Finally, we prove that we may expect the global uniqueness of the optimal control under additional assumptions.

Publisher

Wiley

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1002/mma.10148

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