American Institute of Mathematical Sciences

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January  2010, 26(1): 197-223. doi: 10.3934/dcds.2010.26.197

Front propagation for a two-dimensional periodic monostable lattice dynamical system

Jong-Shenq Guo 1, and  Chang-Hong Wu 1,

1. 

Department of Mathematics, National Taiwan Normal University, 88, S-4, Ting Chou Road, Taipei 11677, Taiwan

Received  October 2008 Revised  August 2009 Published  October 2009

We study the traveling wave front solutions for a two-dimensional periodic lattice dynamical system with monostable nonlinearity. We first show that there is a minimal speed such that a traveling wave solution exists if and only if its speed is above this minimal speed. Then we prove that any wave profile is strictly monotone. Finally, we derive the convergence of discretized minimal speed to the continuous minimal speed.
Keywords: wave profile., monostable, wave speed, traveling wave, Lattice dynamical system.
Mathematics Subject Classification: Primary: 34K05, 34A34; Secondary: 34K60, 34E0.
Citation: Jong-Shenq Guo, Chang-Hong Wu. Front propagation for a two-dimensional periodic monostable lattice dynamical system. Discrete & Continuous Dynamical Systems, 2010, 26 (1) : 197-223. doi: 10.3934/dcds.2010.26.197
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