Existence and uniqueness of traveling waves for non-monotone integral equations with applications

Jian Fang; Xiao Qiang Zhao

doi:10.1016/j.jde.2010.01.009

Existence and uniqueness of traveling waves for non-monotone integral equations with applications

Jian Fang
, Xiao Qiang Zhao^*

^*Corresponding author for this work

School of Mathematics

Memorial University of Newfoundland

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

101 Scopus citations

Abstract

A class of integral equations without monotonicity is investigated. It is shown that there is a spreading speed c^* > 0 for such an integral equation, and that its limiting integral equation admits a unique traveling wave (up to translation) with speed c ≥ c^* and no traveling wave with c < c^*. These results are also applied to some nonlocal reaction-diffusion population models.

Original language	English
Pages (from-to)	2199-2226
Number of pages	28
Journal	Journal of Differential Equations
Volume	248
Issue number	9
DOIs	https://doi.org/10.1016/j.jde.2010.01.009
State	Published - 1 May 2010

Keywords

Existence and uniqueness
Integral equations
Spreading speeds
Traveling waves

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10.1016/j.jde.2010.01.009

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title = "Existence and uniqueness of traveling waves for non-monotone integral equations with applications",

abstract = "A class of integral equations without monotonicity is investigated. It is shown that there is a spreading speed c* > 0 for such an integral equation, and that its limiting integral equation admits a unique traveling wave (up to translation) with speed c ≥ c* and no traveling wave with c < c*. These results are also applied to some nonlocal reaction-diffusion population models.",

keywords = "Existence and uniqueness, Integral equations, Spreading speeds, Traveling waves",

author = "Jian Fang and Zhao, \{Xiao Qiang\}",

year = "2010",

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doi = "10.1016/j.jde.2010.01.009",

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T1 - Existence and uniqueness of traveling waves for non-monotone integral equations with applications

AU - Fang, Jian

AU - Zhao, Xiao Qiang

PY - 2010/5/1

Y1 - 2010/5/1

N2 - A class of integral equations without monotonicity is investigated. It is shown that there is a spreading speed c* > 0 for such an integral equation, and that its limiting integral equation admits a unique traveling wave (up to translation) with speed c ≥ c* and no traveling wave with c < c*. These results are also applied to some nonlocal reaction-diffusion population models.

AB - A class of integral equations without monotonicity is investigated. It is shown that there is a spreading speed c* > 0 for such an integral equation, and that its limiting integral equation admits a unique traveling wave (up to translation) with speed c ≥ c* and no traveling wave with c < c*. These results are also applied to some nonlocal reaction-diffusion population models.

KW - Existence and uniqueness

KW - Integral equations

KW - Spreading speeds

KW - Traveling waves

UR - https://www.scopus.com/pages/publications/77249168810

U2 - 10.1016/j.jde.2010.01.009

DO - 10.1016/j.jde.2010.01.009

M3 - 文章

AN - SCOPUS:77249168810

SN - 0022-0396

VL - 248

SP - 2199

EP - 2226

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 9

ER -

Existence and uniqueness of traveling waves for non-monotone integral equations with applications

Abstract

Keywords

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