AN OPTIMAL CONTROL PROBLEM FOR A LOTKA-VOLTERRA COMPETITION MODEL WITH CHEMO-REPULSION

doi:10.1007/s10473-024-0219-7

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (2): 721-751.doi: 10.1007/s10473-024-0219-7

AN OPTIMAL CONTROL PROBLEM FOR A LOTKA-VOLTERRA COMPETITION MODEL WITH CHEMO-REPULSION

Diana I. HERNÁNDEZ, Diego A. RUEDA-GÓMEZ, Élder J. VILLAMIZAR-ROA^*

Universidad Industrial de Santander, Escuela de Matemáticas, A.A. 678, Bucaramanga, Colombia

收稿日期:2022-11-20 修回日期:2023-01-08 出版日期:2024-04-25 发布日期:2024-04-16
通讯作者: *Élder J. VILLAMIZAR-ROA, E-mail: jvillami@uis.edu.co
基金资助:
Vicerrectoría de Investigación y Extensión of Universidad Industrial de Santander, Colombia, project 3704.

AN OPTIMAL CONTROL PROBLEM FOR A LOTKA-VOLTERRA COMPETITION MODEL WITH CHEMO-REPULSION

Diana I. HERNÁNDEZ, Diego A. RUEDA-GÓMEZ, Élder J. VILLAMIZAR-ROA^*

Universidad Industrial de Santander, Escuela de Matemáticas, A.A. 678, Bucaramanga, Colombia

Received:2022-11-20 Revised:2023-01-08 Online:2024-04-25 Published:2024-04-16
Contact: *Élder J. VILLAMIZAR-ROA, E-mail: jvillami@uis.edu.co
Supported by:
Vicerrectoría de Investigación y Extensión of Universidad Industrial de Santander, Colombia, project 3704.

摘要/Abstract

摘要： 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 $\mathbb{R^N},$ $N=2,3$. 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.

关键词: Lotka-Volterra, chemo-repulsion, optimal control, optimality conditions

Abstract: 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 $\mathbb{R^N},$ $N=2,3$. 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.

Key words: Lotka-Volterra, chemo-repulsion, optimal control, optimality conditions

中图分类号:

35K51

Diana I. HERNÁNDEZ, Diego A. RUEDA-GÓMEZ, Élder J. VILLAMIZAR-ROA. AN OPTIMAL CONTROL PROBLEM FOR A LOTKA-VOLTERRA COMPETITION MODEL WITH CHEMO-REPULSION[J]. 数学物理学报(英文版), 2024, 44(2): 721-751.

Diana I. HERNÁNDEZ, Diego A. RUEDA-GÓMEZ, Élder J. VILLAMIZAR-ROA. AN OPTIMAL CONTROL PROBLEM FOR A LOTKA-VOLTERRA COMPETITION MODEL WITH CHEMO-REPULSION[J]. Acta mathematica scientia,Series B, 2024, 44(2): 721-751.

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AN OPTIMAL CONTROL PROBLEM FOR A LOTKA-VOLTERRA COMPETITION MODEL WITH CHEMO-REPULSION

AN OPTIMAL CONTROL PROBLEM FOR A LOTKA-VOLTERRA COMPETITION MODEL WITH CHEMO-REPULSION

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