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arXiv · 2102.01049

(Un-)bounded transition fronts for the parabolic Anderson model and the randomized F-KPP equation

Jiří Černý·Alexander Drewitz·Lars Schmitz
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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.

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Jiří Černý, Alexander Drewitz, Lars Schmitz. 2021-02-01. (Un-)bounded transition fronts for the parabolic Anderson model and the randomized F-KPP equation. https://arxiv.org/abs/2102.01049

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