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 

机构地区：[1]Universidad Industrial de Santander,Escuela de Matemáticas,A.A.678,Bucaramanga,Colombia

出　　处：《Acta Mathematica Scientia》2024年第2期721-751,共31页数学物理学报（B辑英文版）

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

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.

关 键 词：LOTKA-VOLTERRA chemo-repulsion optimal control optimality conditions 

分 类 号：O232[理学—运筹学与控制论] Q141[理学—数学]