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

Bell, Jonathan

doi:10.1090/qam/614555

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: 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 ${L_p}$-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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