Asymptotic spreading of KPP reactive fronts in heterogeneous shifting environments
Asymptotic spreading of KPP reactive fronts in heterogeneous shifting environments
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DOI：
10.1016/j.matpur.2022.09.001
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发表时间：
2022-10-14
影响因子：
2.3
通讯作者：
Yu, Xiao
中科院分区：
文献类型：
--
作者：
Lam, King-Yeung;Yu, Xiao
通过进一步发展基于汉密尔顿-Jacobi方程粘性解理论的方法，研究了具有任意移动速度的异质移动生境中Kolmogorov-Petrovsky-Piskunov（KPP）锋的渐近传播.我们的框架解决了具有分布时滞的反应扩散方程和积分微分方程。后者导致一类Hamilton-Jacobi型的极限方程依赖于变量x/t，其中时间和空间导数耦合在一起。我们首先建立这些Hamilton-Jacobi方程的唯一性结果，使用基本参数，然后表征的传播速度在一个一维域上的变量s = x/t的约化方程。利用标准的反应扩散型Fisher-KPP方程，给出了环境具有一个或两个移动速度时传播速度的显式表达式。作为副产品，我们还引入了一类新的“渐近齐次”环境，它与相应的齐次环境具有相同的传播速度。(c)2022 Elsevier Masson SAS。All rights reserved.
We study the asymptotic spreading of Kolmogorov-Petrovsky-Piskunov (KPP) fronts in heterogeneous shifting habitats, with any number of shifting speeds, by fur-ther developing the method based on the theory of viscosity solutions of Hamilton -Jacobi equations. Our framework addresses both reaction-diffusion equations and integro-differential equations with a distributed time-delay. The latter leads to a class of limiting equations of Hamilton-Jacobi-type depending on the variable x/t and in which the time and space derivatives are coupled together. We first establish uniqueness results for these Hamilton-Jacobi equations using elementary arguments, and then characterize the spreading speed in terms of a reduced equation on a one-dimensional domain in the variable s = x/t. In terms of the standard Fisher-KPP equation of reaction-diffusion type, we give explicit formulas of the spreading speed when the environment has one or two shifting speeds. As a byproduct, we also in-troduce a novel class of "asymptotically homogeneous" environments which share the same spreading speed with the corresponding homogeneous environments.(c) 2022 Elsevier Masson SAS. All rights reserved.