Exact asymptotic behavior of pulsating traveling waves for a periodic monostable lattice dynamical system

Shi Liang Wu; Guang Sheng Chen; Cheng Hsiung Hsu

doi:10.1090/proc/15369

Exact asymptotic behavior of pulsating traveling waves for a periodic monostable lattice dynamical system

Shi Liang Wu, Guang Sheng Chen, Cheng Hsiung Hsu

Department of Mathematics

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

1 Scopus citations

Abstract

This paper is concerned with the pulsating traveling waves of a periodic lattice dynamical system with monostable nonlinearity. We first establish the exponential upper and lower bounds of the pulsating wave profiles at minus infinity. Then we prove the uniqueness result and derive the asymptotic behavior of all non-critical monostable pulsating traveling waves. This might be the first time to obtain the exact asymptotic behavior of the pulsating traveling waves for periodic discrete systems towards the unstable steady state.

Original language	English
Pages (from-to)	1697-1710
Number of pages	14
Journal	Proceedings of the American Mathematical Society
Volume	149
Issue number	4
DOIs	https://doi.org/10.1090/proc/15369
State	Published - Apr 2021

Keywords

Monostable nonlinearity
Periodic lattice dynamical system
Pulsating traveling wave

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10.1090/proc/15369

Interaction and Stability of Traveling Waves for Lattice Dynamical System and Reaction-Diffusion Equations(3/3)
Hsu, C.
1/08/20 → 31/07/21
Project: Research

Cite this

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N2 - This paper is concerned with the pulsating traveling waves of a periodic lattice dynamical system with monostable nonlinearity. We first establish the exponential upper and lower bounds of the pulsating wave profiles at minus infinity. Then we prove the uniqueness result and derive the asymptotic behavior of all non-critical monostable pulsating traveling waves. This might be the first time to obtain the exact asymptotic behavior of the pulsating traveling waves for periodic discrete systems towards the unstable steady state.

AB - This paper is concerned with the pulsating traveling waves of a periodic lattice dynamical system with monostable nonlinearity. We first establish the exponential upper and lower bounds of the pulsating wave profiles at minus infinity. Then we prove the uniqueness result and derive the asymptotic behavior of all non-critical monostable pulsating traveling waves. This might be the first time to obtain the exact asymptotic behavior of the pulsating traveling waves for periodic discrete systems towards the unstable steady state.

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Exact asymptotic behavior of pulsating traveling waves for a periodic monostable lattice dynamical system

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Keywords

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Projects

Interaction and Stability of Traveling Waves for Lattice Dynamical System and Reaction-Diffusion Equations(3/3)

Cite this