Asymptotic behavior of solutions to 3D Kelvin-Voigt-Brinkman-Forchheimer equations with unbounded delays
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Date
2022-01-17
Authors
Thuy, Le Thi
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article we consider a 3D Kelvin Voigt Brinkman Forchheimer equations involving unbounded delays in a bounded domain Ω ⊂ ℝ3. 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.
Description
Keywords
Kelvin-Voigt-Brinkman-Forchheimer equation, Delay equation, Stationary solution, Local stability, Asymptotically stable, Polynomial stable
Citation
Thuy, L. T. (2022). Asymptotic behavior of solutions to 3D Kelvin-Voigt-Brinkman-Forchheimer equations with unbounded delays. <i>Electronic Journal of Differential Equations, 2022</i>(07), pp. 1-18.
Rights
Attribution 4.0 International