Optimal control for a two-sidedly degenerate aggregation equation
Articles
Mostafa Bendahmane
Université de Bordeaux
https://orcid.org/0000-0001-8570-7088
Fahd Karami
Université Cadi Ayyad
https://orcid.org/0000-0002-1567-4396
Elmahdi Erraji
Université Cadi Ayyad
https://orcid.org/0000-0003-0249-3243
Abdelghafour Atlas
Université Cadi Ayyad
Lekbir Afraites
Université Sultan Moulay Slimane
https://orcid.org/0000-0001-7182-7986
Published 2023-06-04
https://doi.org/10.15388/namc.2023.28.32395
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Keywords

aggregation equation
nonlocal models
degenerate diffusion
finite volume
optimal control
adjoint problem

How to Cite

Bendahmane, M. (2023) “Optimal control for a two-sidedly degenerate aggregation equation”, Nonlinear Analysis: Modelling and Control, 28(4), pp. 780–803. doi:10.15388/namc.2023.28.32395.

Abstract

In this paper, we are concerned with the study of the mathematical analysis for an optimal control of a nonlocal degenerate aggregation model. This model describes the aggregation of organisms such as pedestrian movements, chemotaxis, animal swarming. We establish the wellposedness (existence and uniqueness) for the weak solution of the direct problem by means of an auxiliary nondegenerate aggregation equation, the Faedo–Galerkin method (for the existence result) and duality method (for the uniqueness). Moreover, for the adjoint problem, we prove the existence result of minimizers and first-order necessary conditions. The main novelty of this work concerns the presence of a control to our nonlocal degenerate aggregation model. Our results are complemented with some numerical simulations.

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