Optimal bilinear control problem related to a chemo-repulsion system in 2D domains

Abstract

In this paper we study a bilinear optimal control problem associated to a chemo-repulsion model with linear production term in a bidimensional domain. The existence, uniqueness and regularity of strong solutions of this model are deduced, proving the existence of an global optimal solution. Afterwards, we derive first-order optimality conditions by using a Lagrange multipliers theorem.

Optimal control for the coupled chemotaxis-fluid models in two space dimensions

“…In this section, we will prove the existence of the optimal solution of control problem. The method we use for treating this problem was inspired by some ideas of Guillén-González et al [9]. Assume U ⊂ L 2 (0, T ; H 1 (Ω c )) is a nonempty, closed and convex set, where control domain Ω c ⊂ Ω, and Ω d ⊂ Ω is the observability domain.…”

“…Chen et al [3] studied the distributed optimal control problem for the coupled Allen-Cahn/Cahn-Hilliard equations. Recently, Guillén-González et al [9] studied a bilinear optimal control problem for the chemo-repulsion model with the linear production term. The existence, uniqueness and regularity of strong solutions of this model are deduced.…”

The bang-bang property in some parabolic bilinear optimal control problems \emph{via} two-scale asymptotic expansions

“…); we refer the interested reader to [1,7,12] and the references therein. In the field of bilinear optimal control problems, let us first point to [21,22] for the study of bilinear control problems in connection with chemotaxis or chemorepulsion; another very interesting example of such a problem is studied in [48]. In it, the authors study an optimal control problem for brain tumor growth.…”

An optimal control problem related to a 3D-chemotaxis-Navier-Stokes model

“…However, from the optimal control point of view, the literature related is scarce, and most of the results are devoted to the control theory governed by chemotaxis models without fluids (cf. [14,22,[24][25][26]40]). In these references, the authors proved the existence of optimal controls and derived an optimality system.…”