Effects of Diffusion and Advection on the Smallest Eigenvalue of an Elliptic Operator and Their Applications

被引：60

作者：

Chen, Xinfu ^{[1
]}

Lou, Yuan ^{[2
,3
]}

机构：

[1] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

[2] Ohio State Univ, Dept Math, Columbus, OH 43210 USA

[3] Ohio State Univ, Math Biosci Inst, Columbus, OH 43210 USA

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2012年 / 61卷 / 01期

基金：

美国国家科学基金会;

关键词：

diffusion; advection; smallest eigenvalue; asymptotic behavior; 1ST REAL EIGENVALUE; ASYMPTOTIC-BEHAVIOR; LIMITING PROFILES; SMALL-PARAMETER; EVOLUTION; DISPERSAL; EQUATIONS; DYNAMICS; MODEL;

D O I：

10.1512/iumj.2012.61.4518

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the effects of diffusion and advection on the smallest eigenvalue of an elliptic operator with zero Neumann boundary condition. Various asymptotic behaviors of the smallest eigenvalue, as diffusion and advection coefficients approach zero or infinity, are derived. As an application, these qualitative results yield new insight into the role of turbulent diffusion on the persistence of a sinking phytoplankton species.

引用

页码：45 / 80

页数：36

共 32 条

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[Anonymous], 1975, THEORY PROB APPL

[2] On several conjectures from evolution of dispersal [J].