Existence, uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal

Peter W. Bates; Guangyu Zhao

doi:10.1016/j.jmaa.2006.09.007

Existence, uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal

Peter W. Bates
, Guangyu Zhao

Research output: Contribution to journal › Article › peer-review

194 Scopus citations

Abstract

This paper is concerned with a nonlocal evolution equation which is used to model the spatial dispersal of organisms. We study the existence, uniqueness and stability of the positive steady solution for this nonlocal evolution equation under general conditions. The global dynamics are also investigated and a trichotomy of the global asymptotics is established.

Original language	English
Pages (from-to)	428-440
Number of pages	13
Journal	Journal of Mathematical Analysis and Applications
Volume	332
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2006.09.007
State	Published - Aug 1 2007
Externally published	Yes

ASJC Scopus Subject Areas

Analysis
Applied Mathematics

Keywords

Nonlocal evolution equation
Principal eigenvalue
Resolvent positive operator

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10.1016/j.jmaa.2006.09.007

Cite this

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title = "Existence, uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal",

abstract = "This paper is concerned with a nonlocal evolution equation which is used to model the spatial dispersal of organisms. We study the existence, uniqueness and stability of the positive steady solution for this nonlocal evolution equation under general conditions. The global dynamics are also investigated and a trichotomy of the global asymptotics is established.",

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AU - Bates, Peter W.

AU - Zhao, Guangyu

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N2 - This paper is concerned with a nonlocal evolution equation which is used to model the spatial dispersal of organisms. We study the existence, uniqueness and stability of the positive steady solution for this nonlocal evolution equation under general conditions. The global dynamics are also investigated and a trichotomy of the global asymptotics is established.

AB - This paper is concerned with a nonlocal evolution equation which is used to model the spatial dispersal of organisms. We study the existence, uniqueness and stability of the positive steady solution for this nonlocal evolution equation under general conditions. The global dynamics are also investigated and a trichotomy of the global asymptotics is established.

KW - Nonlocal evolution equation

KW - Principal eigenvalue

KW - Resolvent positive operator

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UR - https://www.scopus.com/pages/publications/34147185183#tab=citedBy

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DO - 10.1016/j.jmaa.2006.09.007

M3 - Article

AN - SCOPUS:34147185183

SN - 0022-247X

VL - 332

SP - 428

EP - 440

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Existence, uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal

Abstract

ASJC Scopus Subject Areas

Keywords

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