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Optimal Boundary Control of the Boussinesq Approximation for Polymeric Fluids

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  • Evgenii S. Baranovskii

    (Voronezh State University)

Abstract

We consider an optimal control problem for non-isothermal steady flows of low-concentrated aqueous polymer solutions in a bounded 3D domain. In this problem, the state functions are the flow velocity and the temperature, while the control function is the heat flux through a given part of the boundary of the flow domain. We obtain sufficient conditions for the existence of weak solutions that minimize a cost functional under a given bounded set of admissible controls. It is shown that the marginal function of the considered control system is lower semi-continuous and the optimal states operator generates a continuous branch in a suitable function space.

Suggested Citation

  • Evgenii S. Baranovskii, 2021. "Optimal Boundary Control of the Boussinesq Approximation for Polymeric Fluids," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 623-645, May.
    • Handle: RePEc:spr:joptap:v:189:y:2021:i:2:d:10.1007_s10957-021-01849-4
    DOI: 10.1007/s10957-021-01849-4
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    References listed on IDEAS

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    1. Exequiel Mallea-Zepeda & Eber Lenes & Elvis Valero, 2018. "Boundary Control Problem for Heat Convection Equations with Slip Boundary Condition," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-14, January.
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    Cited by:

    1. Jincheng Shi & Yan Liu, 2022. "Continuous Dependence for the Boussinesq Equations under Reaction Boundary Conditions in R 2," Mathematics, MDPI, vol. 10(6), pages 1-14, March.
    2. Gennadii Alekseev, 2023. "Analysis of Control Problems for Stationary Magnetohydrodynamics Equations under the Mixed Boundary Conditions for a Magnetic Field," Mathematics, MDPI, vol. 11(12), pages 1-29, June.
    3. Zhendong Luo & Xiangdong Liu & Yihui Zeng & Yuejie Li, 2023. "Existence and Uniqueness of Generalized and Mixed Finite Element Solutions for Steady Boussinesq Equation," Mathematics, MDPI, vol. 11(3), pages 1-14, January.
    4. Hossam A. Nabwey & Aamir Abbas Khan & Muhammad Ashraf & Ahmad M. Rashad & Sumayyah I. Alshber & Miad Abu Hawsah, 2022. "Computational Analysis of the Magnetized Second Grade Fluid Flow Using Modified Fourier and Fick’s Law towards an Exponentially Stretching Sheet," Mathematics, MDPI, vol. 10(24), pages 1-15, December.

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    1. Evgenii S. Baranovskii & Olga Yu. Shishkina, 2024. "Generalized Boussinesq System with Energy Dissipation: Existence of Stationary Solutions," Mathematics, MDPI, vol. 12(5), pages 1-15, March.

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