Feedback Control Problem for Modified Kelvin-Voigt Model

This paper deals with the optimal feedback control problem for the modified Kelvin-Voigt model. The considered model describes the motion of weakly concentrated aqueous polymer solutions. In our case, the control function (the external force) depends on the velocity of the fluid. In such a way, the control is not selected from a finite set of available controls, but belongs to the image of some multi-valued map. The solution for the control problem of fluid motion is a pair: the velocity of the fluid and the control (the density of external forces). Since there can be many such pairs, the concept of optimal solution naturally arises, which gives a minimum to specified cost functional. For the considered optimal feedback control problem the existence theorem on weak solution is proved.