Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 07, pp. 1-18.

Title: Asymptotic behavior of solutions to 3D Kelvin-Voigt-Brinkman-Forchheimer
       equations with unbounded delays
       
Author: Le Thi Thuy (Electric Power Univ., Hanoi, Vietnam)

Abstract:  
In this article we consider a 3D Kelvin Voigt Brinkman Forchheimer equations
involving unbounded delays in a bounded domain $\Omega \subset \mathbb{R}^3$.
First, we show the existence and uniqueness of weak solutions by using the
Galerkin approximations method and the energy method.
Second, we prove the existence and uniqueness of stationary solutions by employing
the Brouwer fixed point theorem. Finally, we study the stability of stationary solutions
via the direct classical approach and the construction of a Lyapunov function.
We also give a sufficient condition for the polynomial stability of the stationary
solution for a special case of unbounded variable delay.

Submitted November 3, 2020. Published January 17, 2022.
Math Subject Classifications: 35B41, 35K65, 35D05
Key Words: Kelvin-Voigt-Brinkman-Forchheimer equation; delay equation;
           stationary solution; local stability; asymptotically stable; polynomial stable.