Long time behaviour of a Cahn–Hilliard system coupled with viscoelasticity
Volume 98 / 2010
Annales Polonici Mathematici 98 (2010), 1-21
MSC: 35K50, 35K60, 35L20, 35Q72.
DOI: 10.4064/ap98-1-1
Abstract
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.
