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Stability of Traveling Waves in Partly Parabolic Systems

Published online by Cambridge University Press:  17 September 2013

A. Ghazaryan ,
Y. Latushkin  and
S. Schecter
A. Ghazaryan*
Affiliation:
Department of Mathematics, Miami University, Oxford, OH 45056 USA
Y. Latushkin
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65211 USA
S. Schecter
Affiliation:
Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC 27695 USA
*
⋆ Corresponding author. E-mail: ghazarar@miamioh.edu
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Abstract

We review recent results on stability of traveling waves in partly parabolic reaction-diffusion systems with stable or marginally stable equilibria. We explain how attention to what are apparently mathematical technicalities has led to theorems that allow one to convert spectral calculations, which are used in the sciences and engineering to study stability of a wave, into detailed, theoretically-based information about the behavior of perturbations of the wave.

Keywords

traveling wavespectral stabilitylinear stabilitynonlinear stabilityexponential weights
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 5: Bifurcations , 2013 , pp. 31 - 47
Copyright
© EDP Sciences, 2013

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