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Lattice differential equations embedded into reaction–diffusion systems

Published online by Cambridge University Press:  13 March 2009

Arnd Scheel  and
Erik S. Van Vleck
Arnd Scheel
Affiliation:
School of Mathematics, University of Minnesota, 206 Church Street SE, Minneapolis, MN 55455, USA ([email protected])
Erik S. Van Vleck
Affiliation:
Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA
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Abstract

We show that lattice dynamical systems naturally arise on infinite-dimensional invariant manifolds of reaction–diffusion equations with spatially periodic diffusive fluxes. The result connects wave-pinning phenomena in lattice differential equations and in reaction–diffusion equations in inhomogeneous media. The proof is based on a careful singular perturbation analysis of the linear part, where the infinite-dimensional manifold corresponds to an infinite-dimensional centre eigenspace.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 1 , February 2009 , pp. 193 - 207
Copyright
Copyright © Royal Society of Edinburgh 2009

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