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

作     者：Diana I.HERNÁNDEZ Diego A.RUEDA-GOMEZ Élder J.VILLAMIZAR-ROA Diana I.HERNÁNDEZ;Diego A.RUEDA-GÓMEZ;Élder J.VILLAMIZAR-ROA

作者机构：Universidad Industrial de SantanderEscuela de MatemáticasA.A.678BucaramangaColombia 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2024年第44卷第2期

页      面：721-751页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

基　　金：supported by Vicerrectoría de Investigación y Extensión of Universidad Industrial de Santander Colombia project 3704. 

主　　题：Lotka-Volterra chemo-repulsion optimal control optimality conditions 

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 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.