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| Transversal Instability for the Thermodiffusive Reaction-Diffusion System |
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Citation： |
Michal KOWALCZYK,Benoit PERTHAME,Nicolas VAUCHELET.Transversal Instability for the Thermodiffusive Reaction-Diffusion System[J].Chinese Annals of Mathematics B,2015,36(5):871~882 |
| Page view： 1165
Net amount： 760 |
Authors： |
Michal KOWALCZYK; Benoit PERTHAME;Nicolas VAUCHELET |
Foundation： |
This work was supported by the FONDECYT Grant
(No.,1130126), the ECOS Project (No.C11E07), the Fondo Basal CMM
and the French ``ANR Blanche'' Project Kibord
(No.ANR-13-BS01-0004) |
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| Abstract： |
The propagation of unstable interfaces is at the origin of
remarkable patterns that are observed in various areas of science as
chemical reactions, phase transitions, and growth of bacterial
colonies. Since a scalar equation generates usually stable waves,
the simplest mathematical description relies on two-by-two
reaction-diffusion systems. The authors' interest is the extension
of the Fisher/KPP equation to a two-species reaction which
represents reactant concentration and temperature when used for
flame propagation, and bacterial population and nutrient
concentration when used in biology.
The authors study circumstances in which instabilities can occur and
in particular the effect of dimension. It is observed numerically
that spherical waves can be unstable depending on the coefficients.
A simpler mathematical framework is to study transversal
instability, which means a one-dimensional wave propagating in two
space dimensions. Then, explicit analytical formulas give
explicitely the range of paramaters for instability. |
Keywords： |
Traveling waves, Stability analysis, Reaction-diffusion equation,
Thermodiffusive system |
Classification： |
35C07, 70K50, 76E17, 80A25, 92C17 |
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