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.
出处
《理论数学》
2017年第4期310-321,共12页
Pure Mathematics
基金
国家自然科学基金(No.11601180,11501238)
国家留学基金(No.201608440052)
广东省自然科学基金(No.2016A030310100,2015A030313574,2014A030313641)
广东省教育厅青年人才创新项目(No.2015KQNCX155)。
