Attractors for partially damped systems of binary mixtures of solids

Abstract

This paper targets the long-time dynamics of a semilinear system modeling a binary mixture of solids with frictional dissipation mechanism acting only on the elastic equation and subjected to nonlinear source term. The coupling gives new contributions to the theory associated with nonlinear dynamics of partially damped semilinear systems of a binary mixture of solids. Using the quasi-stability methods, we prove the existence of a smooth finite-dimensional global attractor irrespective of the wave speeds of the system. Moreover, we establish the existence of exponential attractors.