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Optimal regularity and stability analysis in the $\alpha-$Norm for a class of partial functional differential equations with infinite delay
April  2011, 30(1): 137-167. doi: 10.3934/dcds.2011.30.137

## Existence and uniqueness of traveling waves in a class of unidirectional lattice differential equations

 1 Franklin W. Olin College of Engineering, 1000 Olin Way, Needham, MA 02492-1200, United States 2 Gettysburg College, Department of Mathematics, 300 North Washington St., Gettysburg, PA 17325-1400, United States

Received  October 2009 Revised  November 2010 Published  February 2011

We prove the existence and uniqueness, for wave speeds sufficiently large, of monotone traveling wave solutions connecting stable to unstable spatial equilibria for a class of $N$-dimensional lattice differential equations with unidirectional coupling. This class of lattice equations includes some cellular neural networks, monotone systems, and semi-discretizations for hyperbolic conservation laws with a source term. We obtain a variational characterization of the critical wave speed above which monotone traveling wave solutions are guaranteed to exist. We also discuss non-monotone waves, and the coexistence of monotone and non-monotone waves.
Citation: Aaron Hoffman, Benjamin Kennedy. Existence and uniqueness of traveling waves in a class of unidirectional lattice differential equations. Discrete & Continuous Dynamical Systems - A, 2011, 30 (1) : 137-167. doi: 10.3934/dcds.2011.30.137
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