Existence of traveling wave solutions for density-dependent diffusion competitive systems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-13 DOI:10.1088/1361-6544/ad6acd

Yang Wang, Xuanyu Lv, Fan Liu, Xiaoguang Zhang

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引用次数: 0

Abstract

In this paper we are concerned with the existence of traveling wave solutions for two species competitive systems with density-dependent diffusion. Since the density-dependent diffusion is a kind of nonlinear diffusion and degenerates at the origin, the methods for proving the existence of traveling wave solutions for competitive systems with linear diffusion are invalid. To overcome the degeneracy of diffusion, we construct a nonlinear invariant region Ω near the origin. Then by using the method of phase plane analysis, we prove the existence of traveling wave solutions connecting the origin and the unique coexistence state, when the speed c is large than some positive value. In addition, when one species is density-dependent diffusive while the other is linear diffusive, via the change of variables and the central manifold theorem, we prove the existence of the minimal speed

c∗

. And for

c⩾c∗

, traveling wave solutions connecting the origin and the unique coexistence state still exist. In particular, when

c=c∗

, we find that one component of the traveling wave solution is sharp type while the other component is smooth, which is a different phenomenon from linear diffusive systems and scalar equations.

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密度相关扩散竞争系统行波解的存在性

本文关注的是具有密度依赖性扩散的两物种竞争系统的行波解的存在性。由于密度相关扩散是一种非线性扩散，并且在原点处退化，因此证明线性扩散竞争系统行波解存在性的方法是无效的。为了克服扩散的退化性，我们在原点附近构建了一个非线性不变区域Ω。然后利用相平面分析方法，证明当速度 c 大于某个正值时，存在连接原点和唯一共存状态的行波解。此外，当一种物质是密度依赖性扩散而另一种物质是线性扩散时，通过变量变化和中心流形定理，我们证明了最小速度 c∗ 的存在。而对于 c⩾c∗，连接原点和唯一共存状态的行波解仍然存在。特别是当 c=c∗ 时，我们发现行波解的一个分量是尖锐型的，而另一个分量是平滑型的，这是与线性扩散系统和标量方程不同的现象。

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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.