The threshold phenomena for propagation in fractional Laplacian diffusion equations
Résumé
In this paper, we investigate the threshold phenomenon between extinction and propagation in fractional Laplacian diffusion equations for a class of compactly supported initial data. We provide the first quantitative estimates on the threshold when the reaction nonlinearity is of bistable or ignition type. We mainly use estimates on the fundamental solutions of fractional Laplacian operators together with some accurate upper and lower solutions to show that the solution either propagates or goes extinct.
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