The Existence Problem of Feedback Control for One Fractional Voigt Model

In this paper, we study the feedback control problem for a mathematical model that describes the motion of a viscoelastic fluid with memory along velocity field trajectories. We prove the existence of an optimal control that gives a minimum to a given bounded and semicontinuous from below quality functional. The proof uses the approximation-topological approach, the theory of regular Lagrangian flows, and the theory of topological degree for multivalued vector fields.