PM  >> Vol. 7 No. 4 (July 2017)

    拟单调中立型反应扩散方程行波解的唯一性
    Uniqueness of Traveling Wave Solutions for a Quasi-Monotone Reaction-Diffusion Equation with Neutral Type

  • 全文下载: PDF(458KB) HTML   XML   PP.310-321   DOI: 10.12677/PM.2017.74041  
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作者:  

刘玉彬:惠州学院数学与大数据学院,广东 惠州

关键词:
中立型反应扩散方程行波解拟单调反应项唯一性Reaction-Diffusion Equation with Neutral Type Traveling Wave Solution Quasi-Monotone Reaction Uniqueness

摘要:

本文考虑了具有拟单调反应项的中立型反应扩散方程行波解的唯一性问题。首先通过线性变换将方程化为具有无限离散时滞的反应扩散方程,并利用Ikehara定理得到了无限时滞方程波速 的单调行波解的指数渐近性态,进而得到方程波速 的单调行波解是唯一的(平移意义下),最后根据两类方程的解之间的联系得到了原中立型方程波速 的单调行波解的唯一性(平移意义下)。

In present paper, we focus on the uniqueness of traveling wave solutions for a quasi-monotone reaction-diffusion equation with neutral type. By using the Ikehara’s Theorem, we firstly establish the asymptotic exponent properties of monotone traveling wave solution with speed for the reaction-diffusion equation with a infinite number of delays, which is transformed from the neutral equation by a linear variable transform, and then the uniqueness (up to translation) of monotone traveling wave solution with speed for the transformed equation. Finally, we obtain the uniqueness (up to translation) of monotone traveling wave solution with speed for the neutral equation by using the relation between solutions of the neutral equation and of the transformed equation.

文章引用:
刘玉彬. 拟单调中立型反应扩散方程行波解的唯一性[J]. 理论数学, 2017, 7(4): 310-321. https://doi.org/10.12677/PM.2017.74041

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