Well-posedness and stability analysis for a coupled nonlinear mathematical system for a swelling soil problem with nonlocal energy-type damping
Abstract
In this work, we consider a swelling soil system characterized by nonlocal and nonlinear damping of energy-type. We begin by establishing the well-posedness of the problem using the Galerkin method. Next, by the multiplier method, we investigate the asymptotic behavior of the solutions and find the energy decay is of rate $ \frac{1}{\sqrt{t}} $. We further refine the decay rate into $ \frac{1}{t} $ by employing Nakao's Lemma. In particular, the decay of the solutions follows a polynomial pattern.
Fields of Study & Subjects
Stability and Controllability of Differential Equations
Differential Equations and Boundary Problems
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems - S
- Volume
- 30
- Issue
- 0
- Pages
- 465–486
- Publication date
- 1 January 2026
- Language
- EN