Existence and stability of travelling front solutions for general auto-catalytic chemical reaction systems

Elaine Crooks, Fordyce Davidson, Bogdan Kazmierczak, Gregoire Nadin, Je Chiang Tsai, Y. Li, Y. Wu

研究成果: 雜誌貢獻文章

摘要

This paper is concerned with the existence and stability of travelling front solutions for more general autocatalytic chemical reaction systems u t = duxx-uf(v), vt = vxx + uf(v) with d > 0 and d ≠ 1, where f(v) has super-linear or linear degeneracy at v = 0. By applying Lyapunov-Schmidt decomposition method in some appropriate exponentially weighted spaces, we obtain the existence and continuous dependence of wave fronts with some critical speeds and with exponential spatial decay for d near 1. By applying special phase plane analysis and approximate center manifold theorem, the existence of traveling waves with algebraic spatial decay or with some lower exponential decay is also obtained for d > 0. Further, by spectral estimates and Evans function method, the wave fronts with exponential spatial decay are proved to be spectrally or linearly stable in some suitable exponentially weighted spaces. Finally, by adopting the main idea of proof in [12] and some similar arguments as in [21], the waves with critical speeds or with non-critical speeds are proved to be locally exponentially stable in some exponentially weighted spaces and Lyapunov stable in Cunif space, if the initial perturbation of the waves is small in both the weighted and unweighted norms; the perturbation of the waves also stays small in L 1 norm and decays algebraically in Cunif norm, if the initial perturbation is in addition small in L1 norm.

原文英語
頁(從 - 到)2-17
頁數16
期刊Mathematical Modelling of Natural Phenomena
8
發行號3
DOIs
出版狀態已發佈 - 2013

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics

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