General decay of solutions for a viscoelastic porous system with Kelvin-Voigt damping

Abstract

This study investigates the asymptotic stability of a viscoelastic porous system with Kelvin-Voigt damping. The system under consideration involves coupled equations describing the displacement of the solid elastic material, the volume fraction, and a viscoelastic or memory term. Previous studies have shown that introducing control to one equation of these systems can lead to uniform stability for weak solutions when the wave speeds are equal. However, when the wave propagation speeds differ, the decay rate of classical solutions becomes slower. In this work, we improve previous findings by considering the viscoelastic porous elasticity system with Kelvin-Voigt damping applied to the volume fraction equation. By employing the multiplier method in conjunction with the characteristics of convex functions, we establish a general stability estimate independent of the wave speeds. Our results provide valuable insights into the stability properties of viscoelastic porous systems. This study contributes to the existing literature on the subject and has implications for the analysis and control of such systems in various engineering applications.