The Bramson logarithmic delay in the cane toads equations
Analysis of PDEs
2016-10-12 v1
Abstract
We study a nonlocal reaction-diffusion-mutation equation modeling the spreading of a cane toads population structured by a phenotypical trait responsible for the spatial diffusion rate. When the trait space is bounded, the cane toads equation admits traveling wave solutions [7]. Here, we prove a Bramson type spreading result: the lag between the position of solutions with localized initial data and that of the traveling waves grows as (3/(2 *)) log t. This result relies on a present-time Harnack inequality which allows to compare solutions of the cane toads equation to those of a Fisher-KPP type equation that is local in the trait variable.
Cite
@article{arxiv.1610.03285,
title = {The Bramson logarithmic delay in the cane toads equations},
author = {Emeric Bouin and Christopher Henderson and Lenya Ryzhik},
journal= {arXiv preprint arXiv:1610.03285},
year = {2016}
}