Travelling wave solutions to the KPP equation with branching noise arising from initial conditions with compact support
Probability
2015-08-05 v1
Abstract
We consider the one-dimensional KPP-equation driven by space-time white noise and extend the construction of travelling wave solutions arising from Heavyside initial data from [Tribe, 1996, MR1396765] to non-negative continuous functions with compact support. As an application the existence of travelling wave solutions is used to prove that the support of any solution is recurrent. As a by-product, several upper measures are introduced that allow for a stochastic domination of any solution to the SPDE at a fixed point in time.
Keywords
Cite
@article{arxiv.1508.00687,
title = {Travelling wave solutions to the KPP equation with branching noise arising from initial conditions with compact support},
author = {Sandra Kliem},
journal= {arXiv preprint arXiv:1508.00687},
year = {2015}
}
Comments
28 pages