KPP-Fisher时滞方程的单调波前解
Monotone traveling wavefronts of the KPP-Fisher delayed equation
摘要：
在2000年代初，Gourley（2000），Wu et al.（2001），Ashwin et al.（2002）开始研究延迟Kolmogorov-Petrovskii-Piskunov-Fisher方程的正波前。此后，该模型成为单稳态时滞反应扩散方程行波解研究中最热门的研究对象之一。本文给出了KPP-Fisher方程中单调波的存在唯一性问题的完全解。我们表明，每个单调行波可以通过迭代过程中发现。所提出的方法是基于使用特殊的单调积分算子（这是不同于通常的吴邹算子）和适当的上下解与他们相关联。对无穷远处的最终行进锋的渐近展开的分析是我们方法的另一个关键组成部分。
英文摘要：
In the early 2000's, Gourley (2000), Wu et al. (2001), Ashwin et al. (2002) initiated the study of the positive wavefronts in the delayed Kolmogorov-Petrovskii-Piskunov-Fisher equation. Since then, this model has become one of the most popular objects in the studies of traveling waves for the monostable delayed reaction-diffusion equations. In this paper, we give a complete solution to the problem of existence and uniqueness of monotone waves in the KPP-Fisher equation. We show that each monotone traveling wave can be found via an iteration procedure. The proposed approach is based on the use of special monotone integral operators (which are different from the usual Wu-Zou operator) and appropriate upper and lower solutions associated to them. The analysis of the asymptotic expansions of the eventual traveling fronts at infinity is another key ingredient of our approach.
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