Differential Equations and Computational Simulations III
Electron. J. Diff. Eqns., Conf. 01, 1997, pp. 211-222.

Traveling wave fronts in spatially discrete reaction-diffusion equations on higher dimensional lattices

Xingfu Zou

Abstract:
This paper deals with the existence of traveling wave fronts of spatially discrete reaction-diffusion equations with delay on lattices with general dimension. A monotone iteration starting from an upper solution is established, and the sequence generated from the iteration is shown to converge to a profile function. The main theorem is then applied to a particular equation arising from branching theory.

Published November 12, 1998.
Mathematics Subject Classifications: 34B99,34C37, 34K99, 35K57.
Key words and phrases: spatially discrete, reaction-diffusion equation, delay, lattice, traveling wave front, upper-lower solution.

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Xingfu Zou
Department of Mathematics and Statistics, University of Victoria
Victoria, BC, Canada V8W 3P4
Curent address: Center for Dynamical Systems and Nonlinear Studies
Georgia Institute of Technology
Atlanta, GA 30332-0190, USA.
Email address: xzou@math.gatech.edu
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