抛物型Anderson模型和随机F-KPP方程的（Un-）有界跃迁前沿

IF 1.4 2区数学 Q2 STATISTICS & PROBABILITY

Annals of Applied Probability Pub Date : 2021-02-01 DOI:10.1214/22-aap1869

J. vCern'y, Alexander Drewitz, Lars Schmitz

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引用次数: 3

摘要

我们研究了随机Fisher KPP方程及其线性化抛物型Anderson模型解前沿的一致有界性。众所周知，对于标准（即确定性）Fisher KPP方程，以及具有所谓点火型非线性的随机化Fisher KPP方程式的特殊情况，具有一致有界（在时间上）跃迁前沿。在这里，我们证明了具有一致有界转移前沿的性质不适用于一般随机Fisher KPP方程。然而，我们证明了这个性质对于抛物型Anderson模型是成立的。

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

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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来源期刊

Annals of Applied Probability 数学-统计学与概率论

CiteScore

2.70

自引率

5.60%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The Annals of Applied Probability aims to publish research of the highest quality reflecting the varied facets of contemporary Applied Probability. Primary emphasis is placed on importance and originality.