非单调非局部单稳反应扩散方程的单调波
Monotone waves for non-monotone and non-local monostable reaction-diffusion equations
摘要：
本文提出了非单调非局部单稳Mackey-Glass型扩散方程中单调波前存在性的一个判据。这推广了Gomez等人最近对具有局部时滞反应的方程的特殊情形所证明的结果。此外，我们证明了唯一性（直到一个平移）得到的单调波前的类内的所有单调波前（这样的一种条件唯一性最近建立的非局部KPP-Fisher方程的方和赵）。此外，我们表明，如果延迟反应是本地的，那么这种独特性实际上在所有波前的类内成立，因此所考虑的最小波前（无论是拉或推）应该是单调的。与KPP-Fisher方程的情形类似，我们的方法是基于构造线性积分-微分方程相关边值问题的适当基本解.
英文摘要：
We propose a criterion for the existence of monotone wavefronts in non-monotone and non-local monostable diffusive equations of the Mackey-Glass type. This extends recent results by Gomez et al proved for the particular case of equations with local delayed reaction. In addition, we demonstrate the uniqueness (up to a translation) of obtained monotone wavefront within the class of all monotone wavefronts (such a kind of conditional uniqueness was recently established for the non-local KPP-Fisher equation by Fang and Zhao). Moreover, we show that if delayed reaction is local then this uniqueness actually holds within the class of all wavefronts and therefore the minimal fronts under consideration (either pulled or pushed) should be monotone. Similarly to the case of the KPP-Fisher equations, our approach is based on the construction of an appropriate fundamental solution for associated boundary value problem for linear integral-differential equation.
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