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Boundary Control Problem for Heat Convection Equations with Slip Boundary Condition

Author

Listed:
  • Exequiel Mallea-Zepeda
  • Eber Lenes
  • Elvis Valero

Abstract

We analyze an optimal boundary control problem for heat convection equations in a three-dimensional domain, with mixed boundary conditions. We prove the existence of optimal solutions, by considering boundary controls for the velocity vector and the temperature. The analyzed optimal control problem includes the minimization of a Lebesgue norm between the velocity and some desired field, as well as the temperature and some desired temperature. By using the Lagrange multipliers theorem we derive an optimality system. We also give a second-order sufficient condition.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlmpe:7959761
    DOI: 10.1155/2018/7959761
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    Cited by:

    1. Evgenii S. Baranovskii & Anastasia A. Domnich & Mikhail A. Artemov, 2024. "Mathematical Analysis of the Poiseuille Flow of a Fluid with Temperature-Dependent Properties," Mathematics, MDPI, vol. 12(21), pages 1-19, October.
    2. 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.
    3. 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.

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