Nonlinear delayed porous-elastic system with microtemperatures- Existence, uniqueness and general decay

Abstract

In this paper, we consider a one-dimensional porous-elastic system subjected to microtemperatures effects, with a nonlinear dissipation and a nonlinear delay of the form $h_{2}(u_{t}(t-\tau))$. 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 which was mentioned in many works before or any other condition on the coefficients. Our result is new and improves previous results in the literature.