Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Exponential attractors for nonautonomous first-order evolution equations

Pages: 225 - 240, Volume 4, Issue 2, April 1998      doi:10.3934/dcds.1998.4.225

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Pierre Fabrie - Université Bordeaux-I, Mathématiques Appliquées, 351 Cours de la Libération, 33405 Talence Cedex, France (email)
Alain Miranville - Université de Poitiers, Département de Mathématiques, 40 Avenue du Recteur Pineau, 86022 Poitiers Cedex, France (email)

Abstract: Our aim in this article is to study the existence of exponential attractors for nonautonomous dissipative evolution equations. We follow the approach of Chepyzhov and Vishik, which consists in studying a semigroup on an extended space.

Keywords:  Exponential attractor, nonautonomous system, uniform attractor, Navier-Stokes equations.
Mathematics Subject Classification:  Primary: 35B40, 35B45, 35Q30.

Received: October 1996;      Revised: May 1997;      Available Online: February 1998.