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.