Attractors for gradient flows of nonconvex functionals and applications

This paper addresses the long-time behaviour of gradient flows of nonconvex
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 nonconvex evolution
problems. In particular, we discuss the long-time behaviour of solutions of
quasistationary phase field models and prove the existence of a global attractor.