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    政大機構典藏 > 理學院 > 應用數學系 > 期刊論文 >  Item 140.119/64832


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    題名: The evolution of traveling waves in a simple isothermal chemical system modelling quadratic autocatalysis with strong decay
    作者: Fu, Sheng-Chen
    符聖珍
    Tsai, Je-Chiang
    貢獻者: 應數系
    關鍵詞: Reaction–diffusion system;Traveling wave;Global stability;Isothermal chemical reaction;Quadratic autocatalysis;Strong decay
    日期: 2014.05
    上傳時間: 2014-03-21 18:02:28 (UTC+8)
    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→2B 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.
    關聯: Journal of Differential Equations,256(10), 3335-3364
    資料來源: http://dx.doi.org/10.1016/j.jde.2014.02.009
    資料類型: article
    顯示於類別:[應用數學系] 期刊論文

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