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Attractors for Gradient Flows of Nonconvex Functionals and Applications

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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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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Brescia, via Valotti 9, 25133, Brescia, Italy

    Riccarda Rossi

  2. Weierstrass-Institut für Angewandte Analysis und Stochastik, Mohrenstrasse 39, 10117, Berlin, Germany

    Antonio Segatti

  3. Istituto di Matematica Applicata e Tecnologie Informatiche – CNR, via Ferrata 1, 27100, Pavia, Italy

    Ulisse Stefanelli

Authors
  1. Riccarda Rossi
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  2. Antonio Segatti
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  3. Ulisse Stefanelli
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Correspondence to Riccarda Rossi.

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Communicated by L. Ambrosio

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Rossi, R., Segatti, A. & Stefanelli, U. Attractors for Gradient Flows of Nonconvex Functionals and Applications. Arch Rational Mech Anal 187, 91–135 (2008). https://doi.org/10.1007/s00205-007-0078-0

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