Abstract
We show that lattice dynamical systems naturally arise on infinite-dimensional invariant manifolds of reactiondiffusion equations with spatially periodic diffusive fluxes. The result connects wave-pinning phenomena in lattice differential equations and in reactiondiffusion 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.
Original language | English (US) |
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Pages (from-to) | 193-207 |
Number of pages | 15 |
Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |
Volume | 139 |
Issue number | 1 |
DOIs | |
State | Published - Feb 2009 |
Bibliographical note
Funding Information:This work was partly supported by the National Science Foundation through Grant nos NSF DMS-0504271 (A.S.) and NSF DMS-0513438 (E.V.).