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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

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

Pages: 197 - 223, Volume 26, Issue 1, January 2010      doi:10.3934/dcds.2010.26.197

 
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Jong-Shenq Guo - Department of Mathematics, National Taiwan Normal University, 88, S-4, Ting Chou Road, Taipei 11677, Taiwan (email)
Chang-Hong Wu - Department of Mathematics, National Taiwan Normal University, 88, S-4, Ting Chou Road, Taipei 11677, Taiwan (email)

Abstract: 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:  Lattice dynamical system, monostable, traveling wave, wave speed, wave profile.
Mathematics Subject Classification:  Primary: 34K05, 34A34; Secondary: 34K60, 34E05.

Received: October 2008;      Revised: August 2009;      Available Online: October 2009.