(UN-)BOUNDED TRANSITION FRONTS FOR THE PARABOLIC ANDERSON MODEL AND THE RANDOMIZED F-KPP EQUATION

• 成果类型: Article
• 署名作者: Cerny, Jiri; Drewitz, Alexander; Schmitz, Lars
• 署名单位: University of Basel; University of Cologne
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1869
• 发表日期: 2023
• 页码: 2342-2373
• 关键词: nonexistence; CONVERGENCE; EXISTENCE; waves

摘要

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.