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Spatio-Temporal Dynamics of Reaction-Diffusion Patterns

In: Trends in Nonlinear Analysis

Author

Listed:
  • Bernold Fiedler

    (Freie Universität Berlin, FB Mathematik I)

  • Arnd Scheel

    (University of Minnesota, School of Mathematics)

Abstract

In this survey we look at parabolic partial differential equations from a dynamical systems point of view. With origins deeply rooted in celestial mechanics, and many modern aspects traceable to the monumental influence of Poincaré, dynamical systems theory is mainly concerned with the global time evolution T(t)u 0 of points u 0 — and of sets of such points — in a more or less abstract phase space X. The success of dynamical concepts such as gradient flows, invariant manifolds, ergodicity, shift dynamics, etc. during the past century has been enormous — both as measured by achievement, and by vitality in terms of newly emerging questions and long-standing open problems.

Suggested Citation

  • Bernold Fiedler & Arnd Scheel, 2003. "Spatio-Temporal Dynamics of Reaction-Diffusion Patterns," Springer Books, in: Markus Kirkilionis & Susanne Krömker & Rolf Rannacher & Friedrich Tomi (ed.), Trends in Nonlinear Analysis, chapter 2, pages 23-152, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-05281-5_2
    DOI: 10.1007/978-3-662-05281-5_2
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