On the stability of a nonlinear damped Porous elastic system without temperatures effects

Abstract

In this paper, we consider a one-dimensional porous-elastic system with dissipation due to nonlinear term and microtemperatures effects. It is it is known that such a system with additional damping terms lacks exponential stability unless another damping mechanism is added. In this work, however, We establish an energy decay rate by using a perturbed energy method and some properties of convex functions, but regardless of the wave speeds of the system or any other condition on the coefficients. Our result is new and improves previous results in nonlinearity case.