Quantifying the threshold phenomena for propagation in nonlocal diffusion equations
Analysis of PDEs
2022-01-06 v1
Abstract
We are interested in the threshold phenomena for propagation in nonlocal diffusion equations with some compactly supported initial data. In the so-called 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 sub-and super-solutions.
Cite
@article{arxiv.2201.01512,
title = {Quantifying the threshold phenomena for propagation in nonlocal diffusion equations},
author = {Matthieu Alfaro and Arnaud Ducrot and Hao Kang},
journal= {arXiv preprint arXiv:2201.01512},
year = {2022}
}