An optimal control problem for a Lotka-Volterra competition model with chemo-repulsion

In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain of ℝ ℕ , N = 2, 3. This model describes the competition of two species in which one of them avoid encounters with rivals through a chemo-repulsion mecha...

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Bibliographic Details
Published in:Acta mathematica scientia 2024-03, Vol.44 (2), p.721-751
Main Authors: Hernández, Diana I., Rueda-Gómez, Diego A., Villamizar-Roa, Élder J.
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
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Summary:In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain of ℝ ℕ , N = 2, 3. This model describes the competition of two species in which one of them avoid encounters with rivals through a chemo-repulsion mechanism. We prove the existence and uniqueness of weak-strong solutions, and then we analyze the existence of a global optimal solution for a related bilinear optimal control problem, where the control is acting on the chemical signal. Posteriorly, we derive first-order optimality conditions for local optimal solutions using the Lagrange multipliers theory. Finally, we propose a discrete approximation scheme of the optimality system based on the gradient method, which is validated with some computational experiments.
ISSN:0252-9602
1572-9087
DOI:10.1007/s10473-024-0219-7