Approximations of random dispersal operators/equations by nonlocal dispersal operators/equations

被引：38

作者：

Shen, Wenxian ^{[1
]}

Xie, Xiaoxia ^{[2
]}

机构：

[1] Auburn Univ, Dept Math & Stat, Auburn, AL 36849 USA

[2] IIT, Dept Appl Math, Chicago, IL 60616 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年 / 259卷 / 12期

关键词：

Nonlocal dispersal; Random dispersal; KPP equation; Principal eigenvalue; Principal spectrum point; Positive time periodic solution; SPREADING SPEEDS; PRINCIPAL EIGENVALUES; SPECTRAL THEORY; HEAT-EQUATION; DIFFUSION; EXISTENCE; UNIQUENESS; STABILITY; EVOLUTION; CONVERGENCE;

D O I：

10.1016/j.jde.2015.08.026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper concerns the approximations of random dispersal operators/equations by nonlocal dispersal operators/equations. It first proves that the solutions of properly rescaled nonlocal dispersal initial-boundary value problems converge to the solutions of the corresponding random dispersal initial-boundary value problems. Next, it proves that the principal spectrum points of nonlocal dispersal operators with properly rescaled kernels converge to the principal eigenvalues of the corresponding random dispersal operators. Finally, it proves that the unique positive time periodic solutions of nonlocal dispersal KPP equations with properly rescaled kernels converge to the unique positive time periodic solutions of the corresponding random dispersal KPP equations. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：7375 / 7405

页数：31

共 46 条

[1]

[Anonymous], 1937, B MOSCOW U MATH MECH

[2]

[Anonymous], 2003, WILEY SERIES MATH CO

[3] Uniform convergence for elliptic problems on varying domains [J].