Spatio-Temporal Dynamics of Reaction-Diffusion Patterns

Bernold Fiedler () and Arnd Scheel ()
Additional contact information
Bernold Fiedler: Freie Universität Berlin, FB Mathematik I
Arnd Scheel: University of Minnesota, School of Mathematics

Chapter 2 in Trends in Nonlinear Analysis, 2003, pp 23-152 from Springer

Abstract: 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.

Keywords: Hopf Bifurcation; Global Attractor; Essential Spectrum; Spiral Wave; Morse Index (search for similar items in EconPapers)
Date: 2003
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-05281-5_2

Ordering information: This item can be ordered from
http://www.springer.com/9783662052815

DOI: 10.1007/978-3-662-05281-5_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().