Travelling wave solutions to the KPP equation with branching noise arising from initial conditions with compact support

Sandra Kliem

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arXiv · 1508.00687

Travelling wave solutions to the KPP equation with branching noise arising from initial conditions with compact support

Sandra Kliem

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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.

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Sandra Kliem. 2015-08-04. Travelling wave solutions to the KPP equation with branching noise arising from initial conditions with compact support. https://arxiv.org/abs/1508.00687

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