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Optimal Dirichlet Boundary Control for the Corotational Oldroyd Model

Author

Listed:
  • Evgenii S. Baranovskii

    (Department of Applied Mathematics, Informatics and Mechanics, Voronezh State University, 394018 Voronezh, Russia)

  • Mikhail A. Artemov

    (Department of Applied Mathematics, Informatics and Mechanics, Voronezh State University, 394018 Voronezh, Russia)

Abstract

In this article, we investigate an optimal control problem for the coupled system of partial differential equations describing the steady-state flow of a corotational-type Oldroyd fluid through a bounded 3D (or 2D) domain. The control function is included in Dirichlet boundary conditions for the velocity field; in other words, we consider a model of inflow–outflow control. The main result is a theorem that states sufficient conditions for the solvability of the corresponding optimization problem in the set of admissible weak solutions. Namely, we establish the existence of a weak solution that minimizes the cost functional under given constraints on controls and states.

Suggested Citation

  • Evgenii S. Baranovskii & Mikhail A. Artemov, 2023. "Optimal Dirichlet Boundary Control for the Corotational Oldroyd Model," Mathematics, MDPI, vol. 11(12), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2719-:d:1171999
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