Asymptotic Stability and General Energy Decay for a Swelling Soil Problem With Nonlinear Kelvin–Voigt Damping and Infinite Memory

This paper studies a swelling system with nonlinear Kelvin–Voigt damping and infinite memory. By employing the multiplier method and some properties of convex functions, we establish a general decay result encompassing both exponential and polynomial decays as special cases. We discuss different instances based on the nature of the Kelvin–Voigt damping. This is the first work to address the combined effects of nonlinear Kelvin–Voigt damping and infinite memory in such systems. Our findings not only generalize and extend earlier results in the literature but also pave the way for further exploration and development in this field of research.