On an optimal control problem in the Voigt model of the motion of a viscoelastic fluid

The external feedback control problem in the Voigt model of the motion of a viscoelastic fluid is investigated. To this end, we prove the existence of weak solutions of the initial-boundary problem with the multi-valued right-hand side in the model considered and show the existence of a solution minimizing a given bounded lower semicontinuous functional. __________ Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 16, Differential and Functional Differential Equations. Part 2, 2006.