| Issue |
Math. Model. Nat. Phenom.
Volume 8, Number 5, 2013
Bifurcations
|
|
|---|---|---|
| Page(s) | 31 - 47 | |
| DOI | https://doi.org/10.1051/mmnp/20138503 | |
| Published online | 17 September 2013 | |
Stability of Traveling Waves in Partly Parabolic Systems
1
Department of Mathematics, Miami University,
Oxford, OH 45056
USA
2
Department of Mathematics, University of Missouri,
Columbia, MO 65211
USA
3
Department of Mathematics, North Carolina State
University, Box
8205, Raleigh,
NC 27695
USA
⋆ Corresponding author. E-mail: ghazarar@miamioh.edu
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.
Mathematics Subject Classification: 35K57 / 35B35 / 47D06
Key words: traveling wave / spectral stability / linear stability / nonlinear stability / exponential weights
© EDP Sciences, 2013
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