Traveling wave solution for a lattice dynamical system withconvolution type nonlinearity

Jong-Shenq Guo; Ying-Chih Lin

doi:10.3934/dcds.2012.32.101

Article Contents

2012, Volume 32, Issue 1: 101-124. Doi: 10.3934/dcds.2012.32.101

This issue Previous Article Lefschetz sequences and detecting periodic points Next Article Spectral analysis for transition front solutions in Cahn-Hilliard systems

Traveling wave solution for a lattice dynamical system with convolution type nonlinearity

Jong-Shenq Guo^1, and
Ying-Chih Lin^2,

1.
Department of Mathematics, Tamkang University, 151, Ying-Chuan Road, Tamsui, Taipei County 25137
2.
Department of Mathematics, National Taiwan Normal University, 88, S-4, Ting Chou Road, Taipei 11677

Received: August 2010

Revised: December 2010

Published: January 2012

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Abstract

We study traveling wave solutions for a lattice dynamical system with convolution type nonlinearity. We consider the monostable case and discuss the asymptotic behaviors, monotonicity and uniqueness of traveling wave. First, we characterize the asymptotic behavior of wave profile at both wave tails. Next, we prove that any wave profile is strictly decreasing. Finally, we prove the uniqueness (up to translation) of wave profile for each given admissible wave speed.

Keywords:

Mathematics Subject Classification: Primary: 34K05, 34A34; Secondary: 34K60, 34E05.

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