Depinning transitions in discrete reaction-diffusion equations

Details Depinning transitions in discrete reaction-diffusion equations Depinning transitions in discrete reaction-diffusion equations

2002-08-21

arxiv.org/abs/cond-mat/0208405v1

SIAM J. Appl. Math. 63, 1056-1082 (2003)

Physics

Condensed Matter

Materials Science

27 pages, 12 figures, to appear in SIAM J. Appl. Math

Scientific paper

We consider spatially discrete bistable reaction-diffusion equations that admit wave front solutions. Depending on the parameters involved, such wave fronts appear to be pinned or to glide at a certain speed. We study the transition of traveling waves to steady solutions near threshold and give conditions for front pinning (propagation failure). The critical parameter values are characterized at the depinning transition and an approximation for the front speed just beyond threshold is given.

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