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

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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

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

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