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Asymptotics and Uniqueness of Travelling Waves for Non-Monotone Delayed Systems on 2D Lattices

Published online by Cambridge University Press:  20 November 2018

Zhi-Xian Yu  and
Ming Mei
Zhi-Xian Yu
Affiliation:
College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China e-mail: yzx3411422@163.com; yuzx0902@yahoo.com.cn
Ming Mei
Affiliation:
Department of Mathematics, Champlain College Saint-Lambert, Saint-Lambert, QC, J4P 3P2 Department of Mathematics and Statistics, McGill University, Montreal, QC, H3A 2K6 e-mail: mmei@champlaincollege.qc.ca; mei@math.mcgill.ca
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Abstract.

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We establish asymptotics and uniqueness (up to translation) of travelling waves for delayed $2\text{D}$ lattice equations with non-monotone birth functions. First, with the help of Ikehara’s Theorem, the a priori asymptotic behavior of travelling wave is exactly derived. Then, based on the obtained asymptotic behavior, the uniqueness of the traveling waves is proved. These results complement earlier results in the literature.

Keywords

35K572D lattice systemstraveling wavesasymptotic behavioruniquenessnonmonotone nonlinearity
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 3 , 01 September 2013 , pp. 659 - 672
Copyright
Copyright © Canadian Mathematical Society 2013

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