Super-linear propagation for a general, local cane toads model

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2017-05-11 DOI:10.4171/IFB/409

Christopher Henderson, B. Perthame, P. Souganidis

引用次数: 4

Abstract

We investigate a general, local version of the cane toads equation, which models the spread of a population structured by unbounded motility. We use the thin-front limit approach of Evans and Souganidis in [Indiana Univ. Math. J., 1989] to obtain a characterization of the propagation in terms of both the linearized equation and a geometric front equation. In particular, we reduce the task of understanding the precise location of the front for a large class of equations to analyzing a much smaller class of Hamilton-Jacobi equations. We are then able to give an explicit formula for the front location in physical space. One advantage of our approach is that we do not use the explicit trajectories along which the population spreads, which was a basis of previous work. Our result allows for large oscillations in the motility.

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一般蔗蜍局部模型的超线性传播

我们研究了甘蔗蟾蜍方程的一般，局部版本，它模拟了由无界运动结构的种群的传播。我们使用了印第安纳大学数学学院的Evans和Souganidis的薄前缘极限方法。J.， 1989]用线性化方程和几何前沿方程来获得传播的表征。特别是，我们减少了理解一类大型方程的精确前沿位置的任务，以分析一类更小的汉密尔顿-雅可比方程。然后我们就可以给出一个明确的公式来表示物理空间中的前端位置。我们的方法的一个优点是，我们没有使用人口扩散的明确轨迹，这是以前工作的基础。我们的结果允许运动中的大振荡。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.