Attractors for gradient flows of non convex functionals and applications

Rossi, Riccarda; Segatti, Antonio; Stefanelli, Ulisse

Attractors for gradient flows of non convex functionals and applications

Authors

Rossi, Riccarda

Segatti, Antonio

Stefanelli, Ulisse

Description

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.
46 pages