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

被引：0

作者：

Baranovskii, Evgenii S. ^{[1
]}

Artemov, Mikhail A. ^{[1
]}

Ershkov, Sergey V. ^{[2
,3
]}

Yudin, Alexander V. ^{[3
]}

机构：

[1] Voronezh State Univ, Dept Appl Math Informat & Mech, Voronezh 394018, Russia

[2] Plekhanov Russian Univ Econ, Dept Sci Res, Moscow 117997, Russia

[3] Russian Technol Univ, Inst Adv Technol & Ind Programming, MIREA, Moscow 119454, Russia

来源：

MATHEMATICS | 2025年 / 13卷 / 06期

关键词：

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; QUASI-STATIONARY EQUATIONS; COMPLEX HEAT-TRANSFER; STOKES; FLUID; REFLECTION; MOTION; MODEL;

D O I：

10.3390/math13060967

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 Fr & eacute;chet 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.

引用

页数：18