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  • Ergodic Theory and Dynamical Systems, Volume 31, Issue 6
  • December 2011, pp. 1641-1667

Exponential global attractors for semigroups in metric spaces with applications to differential equations

  • DOI:
  • Published online: 15 March 2011

In this article semigroups in a general metric space V, which have pointwise exponentially attracting local unstable manifolds of compact invariant sets, are considered. We show that under a suitable set of assumptions these semigroups possess strong exponential dissipative properties. In particular, there exists a compact global attractor which exponentially attracts each bounded subset of V. Applications of abstract results to ordinary and partial differential equations are given.

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[1]J. Arrieta , A. N. Carvalho and G. Lozada-Cruz . Dynamics in dumbbell domains II. The limiting problem. J. Differential Equations 247 (2009), 174202.

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[12]G. R. Sell and Y. You . Dynamics of Evolutionary Equations. Springer, New York, 2002.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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