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.

中文翻译：

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非均匀Voigt流体运动模型的最优反馈控制问题

在本文中，我们研究了非均匀Voigt流体运动模型的最优反馈控制问题的弱可解性。该证明基于近似拓扑方法。该方法涉及通过正规化算子包含来近似原始问题，并随之应用拓扑度理论。然后，我们显示了逼近问题的解序列与原始问题的解的收敛性。为此，我们使用独立于先验估计的近似参数。最后，我们证明了成本函数在弱解集上达到了最小值。