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

  Published:2011-08-31
 Printed: Sep 2013
  • Zhi-Xian Yu,
    College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China
  • Ming Mei,
    Department of Mathematics, Champlain College Saint-Lambert, Saint-Lambert, QC, J4P 3P2
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Abstract

We establish asymptotics and uniqueness (up to translation) of travelling waves for delayed 2D 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: 2D lattice systems, traveling waves, asymptotic behavior, uniqueness, nonmonotone nonlinearity 2D lattice systems, traveling waves, asymptotic behavior, uniqueness, nonmonotone nonlinearity
MSC Classifications: 35K57 show english descriptions Reaction-diffusion equations 35K57 - Reaction-diffusion equations
 

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