June 2023 (Un-)bounded transition fronts for the parabolic Anderson model and the randomized F-KPP equation
Jiří Černý, Alexander Drewitz, Lars Schmitz
Author Affiliations +
Ann. Appl. Probab. 33(3): 2342-2373 (June 2023). DOI: 10.1214/22-AAP1869

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, the transition front is uniformly bounded (in time). Here, we show that this property of having a uniformly bounded transition front fails to hold for the general randomized Fisher-KPP equation. In contrast, for the parabolic Anderson model we do establish this property under some assumptions.

Acknowledgments

The final version of this article has benefited from careful refereeing.

Citation

Download Citation

Jiří Černý. Alexander Drewitz. Lars Schmitz. "(Un-)bounded transition fronts for the parabolic Anderson model and the randomized F-KPP equation." Ann. Appl. Probab. 33 (3) 2342 - 2373, June 2023. https://doi.org/10.1214/22-AAP1869

Information

Received: 1 April 2021; Revised: 1 July 2022; Published: June 2023
First available in Project Euclid: 2 May 2023

MathSciNet: MR4583673
zbMATH: 1516.35571
Digital Object Identifier: 10.1214/22-AAP1869

Subjects:
Primary: 35A18 , 35B40 , 60K37
Secondary: 60H15 , 60J80

Keywords: F-KPP equation , Parabolic Anderson model , tightness , transition front , Traveling waves

Rights: Copyright © 2023 Institute of Mathematical Statistics

JOURNAL ARTICLE
32 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

Vol.33 • No. 3 • June 2023
Back to Top