Attractors for Gradient Flows of Nonconvex Functionals and Applications |
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| Authors: | Riccarda Rossi Antonio Segatti Ulisse Stefanelli |
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| Affiliation: | (1) Dipartimento di Matematica, Università di Brescia, via Valotti 9, 25133 Brescia, Italy;(2) Weierstrass-Institut für Angewandte Analysis und Stochastik, Mohrenstrasse 39, 10117 Berlin, Germany;(3) Istituto di Matematica Applicata e Tecnologie Informatiche – CNR, via Ferrata 1, 27100 Pavia, Italy |
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| Abstract: | 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. |
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