Some remarks on segregation of $k$ species in strongly competing systems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-03-11 DOI:10.4171/ifb/458

F. Lanzara, Eugenio Montefusco

引用次数: 3

Abstract

Spatial segregation occurs in population dynamics when k species interact in a highly competitive way. As a model for the study of this phenomenon, we consider the competitiondiffusion system of k differential equations −∆ui(x) = −μui(x) ∑ j 6=i uj(x) i = 1, ..., k in a domain D with appropriate boundary conditions. Any ui represents a population density and the parameter μ determines the interaction strength between the populations. The purpose of this paper is to study the geometry of the limiting configuration as μ −→ +∞ on a planar domain for any number of species. If k is even we show that some limiting configurations are strictly connected to the solution of a Dirichlet problem for the Laplace equation. 2010 Mathematics Subject Classification: Primary 35Bxx, 35J47; Secondary 92D25.

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强竞争系统中物种分离的若干问题

在种群动态中，当k个物种以高度竞争的方式相互作用时，就会发生空间分离。作为研究这一现象的模型，我们考虑了k微分方程的竞争扩散系统-∆ui(x) = - μui(x)∑j 6=i uj(x) i = 1，…，在具有适当边界条件的定义域D中的k。ui表示种群密度，参数μ决定种群之间的相互作用强度。本文的目的是研究平面上任意数量物种的极限位形μ−→+∞的几何性质。如果k是偶数，我们证明了一些极限构型与拉普拉斯方程的狄利克雷问题的解是严格相关的。2010数学学科分类:初级35Bxx、35J47;二次92 d25。

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

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