On a distributed control problem for a coupled chemotaxis-fluid model
A distributed optimal control problem from chemotaxis is studied. The governing equations are the stationary Patlak-Keller-Segel model and the Navier-Stokes equation for incompressible fluids; the objective involves tracking terms and a Hilbert space regularization. In effect, the system is controlled through a distributed force and a coefficient of chemotactic sensitivity, and the aim is to drive the chemical concentration, the cell density, and the velocity field towards prescribed targets. It is proved that the optimal control problem has an optimal solution. Furthermore, first order optimality conditions are derived.
scientific article; zbMATH DE number 6932753
scientific article