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arXiv · 2201.08196

The wave speed of an FKPP equation with jumps via coordinated branching

Tommaso Rosati·András Tóbiás
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Abstract

We consider a Fisher-KPP equation with nonlinear selection driven by a Poisson random measure. We prove that the equation admits a unique wave speed $ \mathfrak{s}> 0 $ given by $\frac{\mathfrak{s}^{2}}{2} = \int_{[0, 1]}\frac{ \log{(1 + y)}}{y} \mathfrak{R}( \mathrm d y)$ where $ \mathfrak{R} $ is the intensity of the impacts of the driving noise. Our arguments are based on upper and lower bounds via a quenched duality with a coordinated system of branching Brownian motions.

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Tommaso Rosati, András Tóbiás. 2022-01-20. The wave speed of an FKPP equation with jumps via coordinated branching. https://arxiv.org/abs/2201.08196

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