Stability Analysis of Viscoelastic Swelling Porous Elastic Soils With Nonlinear Kelvin–Voigt Dampings

ABSTRACT In this paper, we consider the swelling porous elasticity soils with finite memory and nonlinear Kelvin–Voigt damping and study the effect of these two types of damping on the asymptotic stability of the energy function. First, we show that the system is globally well posed by implementing the Faedo–Galerkin method. Then, using very broader assumptions regarding the relaxation function and the behavior of the nonlinear dissipative term near the origin, we establish an explicit and optimal formula for the energy decay rate of this system irrespective of the wave speeds of propagation. For, we utilize a multiplier method in conjunction with properties of some convex functions. As the interaction between the considered dampings has never been studied and the hypotheses are more general than the ones in recent papers, our research work makes a novel contribution and it improves several previous results.