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Spatio-Temporal Dynamics of Reaction-Diffusion Patterns

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Trends in Nonlinear Analysis

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.

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  1. FB Mathematik I, Freie Universität Berlin, Arnimallee 2-6, 14195, Berlin, Germany

    Bernold Fiedler

  2. School of Mathematics, University of Minnesota, 206 Church St. S.E., Minneapolis, MN, 55455, USA

    Arnd Scheel

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  1. Mathematics Department and Center for Scientific Computing, University of Warwick, CV4 7AL, Coventry, UK

    Markus Kirkilionis

  2. Institute of Scientific Computing, University of Heidelberg, Im Neuheimer Feld 368, 69120, Heidelberg, Germany

    Susanne Krömker

  3. Institute of Applied Mathematics, University of Heidelberg, Im Neuheimer Feld 293, 69120, Heidelberg, Germany

    Rolf Rannacher

  4. Department of Mathematics, University of Heidelberg, Im Neuheimer Feld 288, 69120, Heidelberg, Germany

    Friedrich Tomi

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Fiedler, B., Scheel, A. (2003). Spatio-Temporal Dynamics of Reaction-Diffusion Patterns. In: Kirkilionis, M., Krömker, S., Rannacher, R., Tomi, F. (eds) Trends in Nonlinear Analysis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05281-5_2

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