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The Kelvin–Voigt–Brinkman–Forchheimer Equations with Non-Homogeneous Boundary Conditions

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)

  • Sergey V. Ershkov

    (Department of Scientific Researches, Plekhanov Russian University of Economics, 117997 Moscow, Russia
    Institute for Advanced Technologies and Industrial Programming, MIREA—Russian Technological University, 119454 Moscow, Russia)

  • Alexander V. Yudin

    (Institute for Advanced Technologies and Industrial Programming, MIREA—Russian Technological University, 119454 Moscow, Russia)

Abstract

We investigate the well-posedness of an initial boundary value problem for the Kelvin–Voigt–Brinkman–Forchheimer equations with memory and variable viscosity under a non-homogeneous Dirichlet boundary condition. A theorem about the global-in-time existence and uniqueness of a strong solution of this problem is proved under some smallness requirements on the size of the model data. For obtaining this result, we used a new technique, which is based on the operator treatment of the initial boundary value problem with the consequent application of an abstract theorem about the local unique solvability of an operator equation containing an isomorphism between Banach spaces with two kind perturbations: bounded linear and differentiable nonlinear having a zero Fréchet derivative at a zero element. Our work extends the existing frameworks of mathematical analysis and understanding of the dynamics of non-Newtonian fluids in porous media.

Suggested Citation

  • Evgenii S. Baranovskii & Mikhail A. Artemov & Sergey V. Ershkov & Alexander V. Yudin, 2025. "The Kelvin–Voigt–Brinkman–Forchheimer Equations with Non-Homogeneous Boundary Conditions," Mathematics, MDPI, vol. 13(6), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:6:p:967-:d:1612604
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    References listed on IDEAS

    as
    1. Evgenii S. Baranovskii, 2020. "Strong Solutions of the Incompressible Navier–Stokes–Voigt Model," Mathematics, MDPI, vol. 8(2), pages 1-16, February.
    2. 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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