Optimal control for a two-sidedly degenerate aggregation equation
BENDAHMANE, Mostafa
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
Institut de Mathématiques de Bordeaux [IMB]
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Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
Institut de Mathématiques de Bordeaux [IMB]
BENDAHMANE, Mostafa
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
Institut de Mathématiques de Bordeaux [IMB]
< Reduce
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
Institut de Mathématiques de Bordeaux [IMB]
Language
en
Article de revue
This item was published in
Nonlinear Analysis: Modelling and Control. 2023-06-04
Vilnius University Press
English 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, ...Read more >
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 well-posedness (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 concern the presence of a control to our nonlocal degenerate aggregation model. Our results are complemented with some numerical simulations.Read less <
English Keywords
Aggregation equation
Nonlocal models
Degenerate diffusion
Finite volume
Optimal control
Adjoint problem
Origin
Hal imported