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Optimal feedback control problem for inhomogeneous Voigt fluid motion model

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Abstract

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.

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Acknowledgements

The authors are very grateful to an anonymous referee for careful reading of the paper and helpful comments. Funding The research of Victor Zvyagin (Theorem 1.2) was supported by the Russian Science Foundation, Project No. 19-11-00146. The research of Mikhail Turbin (Theorem 1.4) was supported by the Russian Foundation for Basic Research, Project No. 20-01-00051.

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  1. Research Institute of Mathematics, Voronezh State University, Universitetskaya sq. 1, Voronezh, 394018, Russian Federation

    Victor Zvyagin & Mikhail Turbin

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  1. Victor Zvyagin
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Correspondence to Mikhail Turbin.

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Zvyagin, V., Turbin, M. Optimal feedback control problem for inhomogeneous Voigt fluid motion model. J. Fixed Point Theory Appl. 23, 4 (2021). https://doi.org/10.1007/s11784-020-00838-w

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