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October  2015, 35(10): 5107-5131. doi: 10.3934/dcds.2015.35.5107

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

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

Received  May 2014 Revised  January 2015 Published  April 2015

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.
Citation: Zhaoquan Xu, Jiying Ma. Monotonicity, asymptotics and uniqueness of travelling wave solution of a non-local delayed lattice dynamical system. Discrete & Continuous Dynamical Systems - A, 2015, 35 (10) : 5107-5131. doi: 10.3934/dcds.2015.35.5107
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