Optimal feedback control problem for inhomogeneous Voigt fluid motion model

In the present paper, we study weak solvability of the optimal feedback control problem for the inhomogeneous Voigt fluid motion model. The proof is based on the approximation-topological approach. This approach involves the approximation of the original problem by regularized operator inclusion with the consequent application of topological degree theory. Then, we show the convergence of the sequence of solutions for the approximation problem to the solution for the original problem. For this, we use independent on approximation parameter a priori estimates. Finally, we prove that the cost functional achieves its minimum on the weak solution set.