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.
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
.
DOI: 10.1007/s10473-024-0219-7
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