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Depinning transitions in discrete reaction-diffusion equations

Carpio Rodríguez, Ana María and Bonilla , L.L. (2003) Depinning transitions in discrete reaction-diffusion equations. SIAM Journal on applied mathematics, 63 (3). pp. 1056-1082. ISSN 0036-1399

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Abstract

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.


Item Type:Article
Uncontrolled Keywords:Discrete reaction-diffusion equations, traveling wave fronts, propagation failure, wave front depinning
Subjects:Sciences > Mathematics > Differential equations
ID Code:15045
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