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

Evgenii S. Baranovskii (), Mikhail A. Artemov, Sergey V. Ershkov and Alexander V. Yudin
Additional contact information
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
Alexander V. Yudin: Institute for Advanced Technologies and Industrial Programming, MIREA—Russian Technological University, 119454 Moscow, Russia

Mathematics, 2025, vol. 13, issue 6, 1-18

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.

Keywords: integro-differential equations; Kelvin–Voigt–Brinkman–Forchheimer model; variable viscosity; viscoelastic fluid; flow-through problem; non-homogeneous Dirichlet boundary condition; lifting operator; strong solution; existence and uniqueness theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/6/967/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/6/967/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:6:p:967-:d:1612604

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().