A note on the stability of traveling-wave solutions to a class of reaction-diffusion systems

Author:
Jonathan Bell

Journal:
Quart. Appl. Math. **38** (1981), 489-496

MSC:
Primary 35B40; Secondary 35K55, 80A20, 92A15

DOI:
https://doi.org/10.1090/qam/614555

MathSciNet review:
614555

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Abstract | References | Similar Articles | Additional Information

Abstract: Many classes of reaction-diffusion systems have been shown to have traveling-wave solutions. For a class of such systems for which a comparison theorem can be used, we establish a wave stability result which roughly states that these wave solutions are asymptotically stable to perturbations which lie in some weighted -space if their speeds are sufficiently large. We then apply this result to some excitable systems, namely a model of the Belousov-Zhabotinskii reaction, a substrate-inhibition biochemical model, and a class of models recently studied by Fife.

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DOI:
https://doi.org/10.1090/qam/614555

Article copyright:
© Copyright 1981
American Mathematical Society