Monotonicity, asymptotics and uniqueness of travelling wave solution of a non-local delayed lattice dynamical system

Zhaoquan Xu; Jiying Ma

doi:10.3934/dcds.2015.35.5107

Article Contents

2015, Volume 35, Issue 10: 5107-5131. Doi: 10.3934/dcds.2015.35.5107

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Monotonicity, asymptotics and uniqueness of travelling wave solution of a non-local delayed lattice dynamical system

Zhaoquan Xu^1, and
Jiying Ma^2,

1.
Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240
2.
College of Science, University of Shanghai for Science and Technology, Shanghai, 200093

Received: April 30, 2014

Revised: December 31, 2014

Published: September 2015

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Abstract

A delayed lattice dynamical system with non-local diffusion and interaction is considered in this paper. The exact asymptotics of the wave profile at both wave tails is derived, and all the wave profiles are shown to be strictly increasing. Moreover, we prove that the wave profile with a given admissible speed is unique up to translation. These results generalize earlier monotonicity, asymptotics and uniqueness results in the literature.

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Mathematics Subject Classification: Primary: 34K05, 35R10; Secondary: 34K30, 35B40.

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