OPTIMIZATION OF THE MOTION OF A VISCO-ELASTIC FLUID VIA MULTIVALUED TOPOLOGICAL DEGREE METHOD

We consider the application of the topological degree theory for noncompact multivalued vector fields to the problem of existence of an optimal feedback control in the presence of delay for the model of the motion of a visco-elastic fluid satisfying the Voight rheological relation. The notion of a weak solution to the problem is introduced and the operator treatment of the problem allows to reduce it to the existence of a fixed point for a certain condensing multivalued map. We give an a priori estimate for solutions of the problem and the use of the degree method allows to prove the non-voidness and compactness of the solution set. As the result we obtain the existence of a solution minimizing the given quality functional.