Journal
SIAM JOURNAL ON APPLIED MATHEMATICS
Volume 63, Issue 3, Pages 1056-1082Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S003613990239006X
Keywords
discrete reaction-diffusion equations; traveling wave fronts; propagation failure; wave front depinning
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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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