Long time behaviour of a Cahn–Hilliard system coupled with viscoelasticity
The long-time behaviour of a unique regular solution to the Cahn–Hilliard system coupled with viscoelasticity is studied. The system arises as a model of the phase separation process in a binary deformable alloy. It is proved that for a sufficiently regular initial data the trajectory of the solution converges to the $\omega $-limit set of these data. Moreover, it is shown that every element of the $\omega $-limit set is a solution of the corresponding stationary problem.