Existence Theorem for a Weak Solution of the Optimal Feedback Control Problem for the Modified Kelvin–Voigt Model of Weakly Concentrated Aqueous Polymer Solutions
- Authors: Plotnikov P.I.1, Turbin M.V.1, Ustiuzhaninova A.S.1
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Affiliations:
- Voronezh State University
- Issue: Vol 100, No 2 (2019)
- Pages: 433-435
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225714
- DOI: https://doi.org/10.1134/S1064562419050089
- ID: 225714
Cite item
Abstract
A theorem on the existence of a weak solution of the optimal feedback control problem for the modified Kelvin–Voigt model of weakly concentrated aqueous polymer solutions is proved. The proof is based on an approximation-topological approach to the study of fluid dynamic problems. At the first step, the considered feedback control problem is interpreted as an operator inclusion with a multivalued right-hand side. At the second step, the resulting inclusion is approximated by an operator inclusion with better properties. Then the existence of solutions for this inclusion is proved by applying a priori estimates of solutions and the degree theory for a class of multivalued mappings. At the third step, it is shown that the sequence of solutions of the approximation inclusion contains a subsequence that converges weakly to the solution of the original inclusion. Finally, it is proved that, among the solutions of the considered problem, there exists at least one minimizing a given cost functional.
About the authors
P. I. Plotnikov
Voronezh State University
Email: mrmike@mail.ru
Russian Federation, Voronezh, 394006
M. V. Turbin
Voronezh State University
Author for correspondence.
Email: mrmike@mail.ru
Russian Federation, Voronezh, 394006
A. S. Ustiuzhaninova
Voronezh State University
Email: mrmike@mail.ru
Russian Federation, Voronezh, 394006