Year: 2026
Type: article
Abstract: In this work, we study a one-dimensional coupled hyperbolic–parabolic system modeling the dynamics of swelling soils under thermodiffusion effects. The model describes the interaction between the deformation of the solid skeleton, the pore fluid motion, the temperature variation, and a diffusive process formulated through chemical potential. Under mixed boundary conditions and without introducing additional mechanical damping or imposing restrictive relations among the physical parameters, we prove exponential stability of the system. Our analysis is based on the energy method. In contrast to the standard energy functional commonly used in related thermodiffusion models, we introduce a modified positive energy functional better adapted to the coupled structure of the system. By combining this energy with suitable auxiliary functionals, we construct an appropriate Lyapunov functional and derive an exponential stability estimate. Our result shows that thermodiffusion alone yields sufficient dissipation for exponential stabilization, complementing earlier works where exponential stability requires extra damping mechanisms or equal wave-speed assumptions.
Source: Mathematics
DOI: 10.3390/math14071184
Authors: Arar Mutlag A. Alajmi, Tijani A. Apalara
Institution: University of Hafr Al-Batin
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7147180206