Quantifying the threshold phenomena for propagation in nonlocal diffusion equations
Abstract
We are interested in the threshold phenomena for propagation in nonlocal diffusion equations with some compactly supported initial data. In the socalled bistable and ignition cases, we provide the first quantitative estimates for such phenomena. The outcomes dramatically depend on the tails of the dispersal kernel and can take a large variety of different forms. The strategy is to combine sharp estimates of the tails of the sum of i.i.d. random variables (coming, in particular, from large deviation theory) and the construction of accurate suband supersolutions.
 Publication:

arXiv eprints
 Pub Date:
 January 2022
 arXiv:
 arXiv:2201.01512
 Bibcode:
 2022arXiv220101512A
 Keywords:

 Mathematics  Analysis of PDEs