Asymptotic Behavior of Solutions for a Lattice System Generated by Non-Autonomous Complex Flows Modeling Concentrated Suspensions

This paper studies the dynamics of concentrated suspensions under shear flow using a non-autonomous mode-coupling model. The model describes the evolution of the stress distribution in a material composed of mesoscopic blocks, incorporating stress relaxation and diffusion effects. We construct an approximating lattice dynamical system for the model under consideration and prove the existence of a compact uniform attractor for the family of semi-processes generated by solutions of the system.