Quasi-stability and smooth global attractors for a elasticity-viscoporosity system with nonlinear damping and source of critical exponents

In this paper we study the long-time dynamics of elasticity-viscoporosity system consisting of two coupled hyperbolic equations with nonlinear dissipation. The first equation of the system is vectorial while the second is scalar. By considering nonlinear dampings and sources of critical exponents, we establish the existence of a smooth finite dimensional global attractor. To our best knowledge, the existence of attractors for dynamics of elasticity-viscoporosity systems has not been studied before.