The evolution of traveling waves in a simple isothermal chemical system modeling quadratic autocatalysis with strong decay

Sheng Chen Fu, Je Chiang Tsai

研究成果: 雜誌貢獻文章

5 引文 斯高帕斯(Scopus)

摘要

In this paper, we study a reaction-diffusion system for an isothermal chemical reaction scheme governed by a quadratic autocatalytic step A+. B→2. B and a decay step B→. C, where A, B, and C are the reactant, the autocatalyst, and the inner product, respectively. Previous numerical studies and experimental evidences demonstrate that if the autocatalyst is introduced locally into this autocatalytic reaction system where the reactant A initially distributes uniformly in the whole space, then a pair of waves will be generated and will propagate outwards from the initial reaction zone. One crucial feature of this phenomenon is that for the strong decay case, the formation of waves is independent of the amount of the autocatalyst B introduced into the system. It is this phenomenon of KPP-type which we would like to address in this paper. To study the propagation of reactant and autocatalyst analytically, we first use the tail behavior of waves to construct a pair of generalized super-/sub-solutions for the approximate system of the autocatalytic reaction system. Note that the autocatalytic reaction system does not enjoy comparison principle. Together with a family of truncated problems, we can establish the existence of a family of traveling waves with the minimal speed. Second, we use this pair of generalized super-/sub-solutions to show that the propagation of waves is fully determined by the rate of decay of the initial data at infinity in the sense of Aronson-Weinberger formulation, which in turn confirms the aforementioned numerical and experimental results.

原文英語
頁(從 - 到)3335-3364
頁數30
期刊Journal of Differential Equations
256
發行號10
DOIs
出版狀態已發佈 - 2014 五月 15

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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