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

Jong-Shenq Guo; Chang-Hong Wu

doi:10.3934/dcds.2010.26.197

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2010, Volume 26, Issue 1: 197-223. Doi: 10.3934/dcds.2010.26.197

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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

Received: September 30, 2008

Revised: July 31, 2009

Published: February 2010

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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.

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Mathematics Subject Classification: Primary: 34K05, 34A34; Secondary: 34K60, 34E05.

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