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

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 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.