Long-time stabilization of solutions to a phase-field model with memory (Q5930661)

A phase-field model with memory terms is studied. It is shown that the globally defined (classical) solution of this problem converges to a solution of the stationary problem (as \(t \rightarrow \infty\)). Some a priori estimates give some information on the structure of the \(\omega\)-limit sets. Because of the memory effects, the energy is not a Lyapunov function for the problem and the set of equilibria may contain a nontrivial continuum of stationary states.