Asymptotic stability of monostable wavefronts in discrete-time integral recursions

Guo Lin; Wan Tong Li; Shi Gui Ruan

doi:10.1007/s11425-009-0123-6

Asymptotic stability of monostable wavefronts in discrete-time integral recursions

Guo Lin, Wan Tong Li, Shi Gui Ruan

Mathematics

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

8 Scopus citations

Abstract

The aim of this work is to study the traveling wavefronts in a discrete-time integral recursion with a Gauss kernel in ℝ². We first establish the existence of traveling wavefronts as well as their precise asymptotic behavior. Then, by employing the comparison principle and upper and lower solutions technique, we prove the asymptotic stability and uniqueness of such monostable wavefronts in the sense of phase shift and circumnutation. We also obtain some similar results in ℝ.

Original language	English (US)
Pages (from-to)	1185-1194
Number of pages	10
Journal	Science China Mathematics
Volume	53
Issue number	5
DOIs	https://doi.org/10.1007/s11425-009-0123-6
State	Published - May 2010

Keywords

Comparison principle
Discrete-time integral recursion
Monostable wave
Stability
Upper and lower solutions

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s11425-009-0123-6

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title = "Asymptotic stability of monostable wavefronts in discrete-time integral recursions",

abstract = "The aim of this work is to study the traveling wavefronts in a discrete-time integral recursion with a Gauss kernel in ℝ2. We first establish the existence of traveling wavefronts as well as their precise asymptotic behavior. Then, by employing the comparison principle and upper and lower solutions technique, we prove the asymptotic stability and uniqueness of such monostable wavefronts in the sense of phase shift and circumnutation. We also obtain some similar results in ℝ.",

keywords = "Comparison principle, Discrete-time integral recursion, Monostable wave, Stability, Upper and lower solutions",

author = "Guo Lin and Li, {Wan Tong} and Ruan, {Shi Gui}",

note = "Funding Information: Acknowledgements This work was partially supported by National Natural Science Foundation of China (Grant No. 10871085) and US National Science Foundation (Grant Nos. DMS-0412047, DMS-0715772).",

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T1 - Asymptotic stability of monostable wavefronts in discrete-time integral recursions

AU - Lin, Guo

AU - Li, Wan Tong

AU - Ruan, Shi Gui

N1 - Funding Information: Acknowledgements This work was partially supported by National Natural Science Foundation of China (Grant No. 10871085) and US National Science Foundation (Grant Nos. DMS-0412047, DMS-0715772).

PY - 2010/5

Y1 - 2010/5

N2 - The aim of this work is to study the traveling wavefronts in a discrete-time integral recursion with a Gauss kernel in ℝ2. We first establish the existence of traveling wavefronts as well as their precise asymptotic behavior. Then, by employing the comparison principle and upper and lower solutions technique, we prove the asymptotic stability and uniqueness of such monostable wavefronts in the sense of phase shift and circumnutation. We also obtain some similar results in ℝ.

AB - The aim of this work is to study the traveling wavefronts in a discrete-time integral recursion with a Gauss kernel in ℝ2. We first establish the existence of traveling wavefronts as well as their precise asymptotic behavior. Then, by employing the comparison principle and upper and lower solutions technique, we prove the asymptotic stability and uniqueness of such monostable wavefronts in the sense of phase shift and circumnutation. We also obtain some similar results in ℝ.

KW - Comparison principle

KW - Discrete-time integral recursion

KW - Monostable wave

KW - Stability

KW - Upper and lower solutions

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JF - Science China Mathematics

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Asymptotic stability of monostable wavefronts in discrete-time integral recursions

Abstract

Keywords

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