(Un-)bounded transition fronts for the parabolic Anderson model and the randomized F-KPP equation
Analysis of PDEs
2021-02-02 v1 Probability
Abstract
We investigate the uniform boundedness of the fronts of the solutions to the randomized Fisher-KPP equation and to its linearization, the parabolic Anderson model. It has been known that for the standard (i.e. deterministic) Fisher-KPP equation, as well as for the special case of a randomized Fisher-KPP equation with so-called ignition type nonlinearity, one has a uniformly bounded (in time) transition front. Here, we show that this property of having a uniformly bounded transition front fails to hold for the general randomized Fisher-KPP equation. Nevertheless, we establish that this property does hold true for the parabolic Anderson model.
Keywords
Cite
@article{arxiv.2102.01049,
title = {(Un-)bounded transition fronts for the parabolic Anderson model and the randomized F-KPP equation},
author = {Jiří Černý and Alexander Drewitz and Lars Schmitz},
journal= {arXiv preprint arXiv:2102.01049},
year = {2021}
}