Spreading speeds for nonlocal Fisher-KPP equations with time-dependent asymmetric kernels
Abstract
In this paper, we establish spreading speeds for a nonlocal Fisher-KPP equation with measurable time-dependent asymmetric kernels, without imposing an inequality between growth and diffusion or requiring the kernel to be positive near the origin. The kernel has a time independent upper bound which is thin-tailed. Both the kernel and the linear growth rate have uniform means. Under these assumptions, we determine the exact rightward and leftward spreading speeds and prove convergence to the positive equilibrium inside the spreading interval. The proof is based on comparison arguments and a family of compactly supported subsolutions. Explicit examples show that time-dependent dispersal kernels with the same time average can exhibit different propagation behaviors.
Related
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BibTeX
@misc{jin2026spreading,
title = {{Spreading speeds for nonlocal Fisher-KPP equations with time-dependent asymmetric kernels}},
author = {Zhucheng Jin and Tao Zhou},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2606.15226},
eprint = {2606.15226},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.15226},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spreading speeds for nonlocal Fisher-KPP equations with time-dependent asymmetric kernels
AU - Zhucheng Jin
AU - Tao Zhou
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2606.15226
UR - https://arxiv.org/abs/2606.15226
AB - In this paper, we establish spreading speeds for a nonlocal Fisher-KPP equation with measurable time-dependent asymmetric kernels, without imposing an inequality between growth and diffusion or requiring the kernel to be positive near the origin. The kernel has a time independent upper bound which is thin-tailed. Both the kernel and the linear growth rate have uniform means. Under these assumptions, we determine the exact rightward and leftward spreading speeds and prove convergence to the positive equilibrium inside the spreading interval. The proof is based on comparison arguments and a family of compactly supported subsolutions. Explicit examples show that time-dependent dispersal kernels with the same time average can exhibit different propagation behaviors.
ER -