On a distributed control problem for a coupled chemotaxis-fluid model

Abstract

In this paper we analyze an optimal distributed control problem where the state equations are given by a stationary chemotaxis model coupled with the Navier-Stokes equations. We consider that the movement and the interaction of cells are occurring in a smooth bounded domain of R n , n = 2, 3, subject to homogeneous boundary conditions. We control the system through a distributed force and a coefficient of chemotactic sensitivity, leading the chemical concentration, the cell density, and the velocity field towards a given target concentration, density and velocity, respectively. In addition to the existence of optimal solution, we derive some optimality conditions.

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

“…However, as far as we know, optimal control problems for evolutive attractive chemotaxis-Navier-Stokes models have not been studied previously. In [39] the authors analyze an optimal distributed control problem where the state equations are given by a stationary chemotaxis model coupled with the Navier-Stokes equations. The control was given through a distributed force and a coefficient of chemotactic sensitivity, leading the chemical concentration, the cell density, and the velocity field towards a given target concentration, density and velocity, respectively.…”

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

“…In the context of optimal control problems associated to chemotaxis models, the literature is also scarce, see [8,10,19,21,22]. In [8] the authors study a distributed optimal control for a twodimensional model of cancer invasion.…”

“…The existence of optimal solutions is proved. In the recent work [19], the authors analyze a distributive optimal control problem where the state equations are given by a stationary chemotaxis model coupled with the Navier-Stokes equations (chemotaxis-fluid system). They prove the existence of an optimal solution.…”

On a bi-dimensional chemo-repulsion model with nonlinear production

“…Not much is known about control problems with state equations given by chemotaxis models (see [1,6,18,19]). In [1] the authors study a distributed optimal control for a two-dimensional model of cancer invasion; the authors prove the existence of optimal solution and derive an optimality system.…”

“…In [19], the authors studied an optimal control problem related to the Keller-Segel system to describe the aggregation process of the cellular slime molds by chemical attraction (see also [20]). In [18], the authors analyze a distributive optimal control problem where the state equations are given by a stationary chemo-atraction model coupled with the Navier-Stokes equations; the system is controlled through a distributed force and a coefficient of chemotactic sensitivity. The auhors prove existence of optimal solution, and derive some optimality conditions.…”