The work is devoted to the study of weak solvability of the optimal feedback control problem for the Voigt model with variable density. The proof is based on the approximation-topological approach. First, the solvability of the approximation problem is proved, and then, based on a priori estimates that are independent of the approximation parameter, it is shown that from the sequence of solutions of the approximation problem, a subsequence converging to the solution of the original problem can be chosen. Then it is shown that among weak solutions to the problem there is at least one that gives a minimum to a given cost functional.

中文翻译：

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变密度Voigt模型的最优反馈控制问题

这项工作致力于研究可变密度的Voigt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。首先，证明了该近似问题的可解性，然后，基于与该近似参数无关的先验估计，表明从该近似问题的解序列中，一个子序列收敛于原始解的解。问题可以选择。然后表明，在对该问题的较弱解决方案中，至少有一个对给定成本函数具有最小限度。