  This paper addresses the long-time behavior of gradient flows of non convex
functionals in Hilbert spaces. Exploiting the notion of generalized semiflows
by J. M. Ball, we provide some sufficient conditions for the existence of a
global attractor. The abstract results are applied to various classes of non
convex evolution problems. In particular, we discuss the long-time behavior of
solutions of quasi-stationary phase field models and prove the existence of a
global attractor.
