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Weak Solvability of the Nonlinearly Viscous Pavlovskii Model

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Abstract

This paper is devoted to studying the solvability of one initial boundary value problem describing the motion of aqueous solutions of polymers. This model considers a nonlinearly viscous fluid. The existence of weak solutions for the considered problem is considered on the basis of a topological approximation approach. In addition, the problem of optimal feedback control is considered for the studied mathematical model. The existence of the optimal solution providing a minimum for the specified bounded and semicontinuous quality functional is proven.

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Funding

This study was performed under support of the Russian Scientific Foundation (grant no. 21-71-00038, https://rscf.ru/project/21-71-00038/) at Voronezh State University (the results of Theorem 1) and the Russian Foundation for Basic Research (grant no. 19-31-60014) at Voronezh State Pedagogical University (the results of Theorem 3).

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Authors and Affiliations

  1. Voronezh State University, 394018, Voronezh, Russia

    A. V. Zvyagin

  2. Voronezh State Pedagogical University, 394043, Voronezh, Russia

    A. V. Zvyagin

Authors
  1. A. V. Zvyagin
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Correspondence to A. V. Zvyagin.

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The author declares that he has no conflicts of interest.

Additional information

Short communication presented by V.G. Zvaygin

Translated by E. Glushachenkova

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Zvyagin, A.V. Weak Solvability of the Nonlinearly Viscous Pavlovskii Model. Russ Math. 66, 73–78 (2022). https://doi.org/10.3103/S1066369X22060093

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