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

  • ALEXANDRE N. CARVALHO (a1) and JAN W. CHOLEWA (a2)
Abstract
Abstract

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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[7] J. W. Cholewa and T. Dlotko . Global Attractors in Abstract Parabolic Problems. Cambridge University Press, Cambridge, 2000.

[10] O. Ladyzenskaya . Attractors for Semigroups and Evolution Equations. Cambridge University Press, Cambridge, 1991.

[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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