Long-time dynamics for nonlinear porous thermoelasticity with second sound and delay

This paper is concerned with the long-time behavior of a damped porous thermoelastic problem. It has been studied by many authors and most of the known results are concerned with decay issues under different boundary conditions and damping terms. There are just a few references on the long-time dynamics of such systems. The purpose of the present work is to complement and extend some early studies on porous thermoelastic systems by establishing new results on the existence of attractors and some of their properties. Motivated by this scenario, we consider a one-dimensional porous thermoelastic system with linear frictional damping, nonlinear source terms, and a time-varying delay term in the internal feedback, where the heat flux depends on Cattaneo' law. Under some suitable assumptions on the weights of feedback, we establish the global well-posedness of the system by using the C-0-semigroup theory of linear operators. Then we show the existence of a global attractor for finite energy solutions and we prove its smoothness and finite fractal dimension. Furthermore, the existence of a generalized fractal exponential attractor is also derived. Published by AIP Publishing.