PreprintCC BY-NC-SA 4.0arXiv
Large time behaviour in the multidimensional nonlocal Fisher-KPP equation
Abstract
This work studies the expansion of the level sets of the solutions of a Fisher-KPP type reaction- diffusion equation, the diffusion being given by a nonnegative, compactly supported, even kernel. Because the latter is not assumed to be spherically symmetric, the level sets advance at an asymptotic speed given by a Freidlin-Gärtner type formula. The main contribution of this paper is to push the expansion up to terms that vanish as time goes to infinity, consisting in an asymptotically logarithmic delay corrected by an function that is constant in time, but depends on the direction of propagation.
Related
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- Spreading speeds for nonlocal Fisher-KPP equations with time-dependent asymmetric kernels
- Nonlocal Fisher--KPP propagation with heavy tails
BibTeX
@misc{roquejoffre2026large,
title = {{Large time behaviour in the multidimensional nonlocal Fisher-KPP equation}},
author = {Jean-Michel Roquejoffre and Mingmin Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32051},
eprint = {2609.32051},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32051},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Large time behaviour in the multidimensional nonlocal Fisher-KPP equation
AU - Jean-Michel Roquejoffre
AU - Mingmin Zhang
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.32051
UR - https://arxiv.org/abs/2609.32051
AB - This work studies the expansion of the level sets of the solutions of a Fisher-KPP type reaction- diffusion equation, the diffusion being given by a nonnegative, compactly supported, even kernel. Because the latter is not assumed to be spherically symmetric, the level sets advance at an asymptotic speed given by a Freidlin-Gärtner type formula. The main contribution of this paper is to push the expansion up to terms that vanish as time goes to infinity, consisting in an asymptotically logarithmic delay corrected by an function that is constant in time, but depends on the direction of propagation.
ER -