The speed of propagation for KPP type problems. I: Periodic framework
The speed of propagation for KPP type problems. I: Periodic framework
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DOI：
10.4171/jems/26
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发表时间：
2005-06
影响因子：
2.6
通讯作者：
Henry Berestycki;François Hamel;Nikolai Nadirashvili
中科院分区：
文献类型：
--
作者：
Henry Berestycki;François Hamel;Nikolai Nadirashvili
本文研究了具有Kolmogorov-Petrovsky-Piskunov （KPP）型非线性的反应扩散方程在周期域和更一般域上的一些非线性传播现象。具有周期性底层可激发介质的周期性域的情况是文章\cite{bh}的后续内容。证明了脉动锋的最小速度由一个包含线性特征值问题的变分公式给出。给出了区域几何形状对反应系数、平流系数和扩散系数影响的一些结论。最后一节讨论渐近扩散速度的概念。给出了扩散速度的主要性质。其中一些是基于无界区域内非线性椭圆方程的一些新的Liouville型结果。
This paper is devoted to some nonlinear propagation phenomena in periodic and more general domains, for reaction-diffusion equations with Kolmogorov-Petrovsky-Piskunov (KPP) type nonlinearities. The case of periodic domains with periodic underlying excitable media is a follow-up of the article \cite{bh}. It is proved that the minimal speed of pulsating fronts is given by a variational formula involving linear eigenvalue problems. Some consequences concerning the influence of the geometry of the domain, of the reaction, advection and diffusion coefficients are given. The last section deals with the notion of asymptotic spreading speed. The main properties of the spreading speed are given. Some of them are based on some new Liouville type results for nonlinear elliptic equations in unbounded domains.