Quantitative estimates of the threshold phenomena for propagation in reaction-diffusion equations
Analysis of PDEs
2019-10-10 v1
Abstract
We focus on the (sharp) threshold phenomena arising in some reaction-diffusion equations supplemented with some compactly supported initial data. In the so-called ignition and bistable cases, we prove the first sharp quantitative estimate on the (sharp) threshold values. Furthermore, numerical explorations allow to conjecture some refined estimates. Last we provide related results in the case of a degenerate monostable nonlinearity "not enjoying the hair trigger effect". AMS Subject Classifications: 35K57 (Reaction-diffusion equations), 35K15 (Initial value problems for second-order parabolic equations), 35B40 (Asymptotic behavior of solutions).
Cite
@article{arxiv.1910.04016,
title = {Quantitative estimates of the threshold phenomena for propagation in reaction-diffusion equations},
author = {Matthieu Alfaro and Arnaud Ducrot and Gregory Faye},
journal= {arXiv preprint arXiv:1910.04016},
year = {2019}
}