PreprintCC BY 4.0HAL
Sharp asymptotics for a transport model with a nonlocal condition of the Fisher-KPP type at the boundary
Abstract
This paper is concerned with the precise asymptotics, as time goes to infinity, of a transport problem in a half plane coupled with a nonlinear nonlocal boundary condition. This system arises from a class of models for the spatial spread of epdemics, its space independent version being the classical Kermack-McKendrick model. Using ideas pertaining to the study of nonlocal equations of the Fisher-KPP type, and exploiting the particular structure of the model, we prove that any initially localized solution will lag behind the minimal traveling wave, with a delay that grows logarithmically in time.
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BibTeX
@misc{faye2026sharp,
title = {{Sharp asymptotics for a transport model with a nonlocal condition of the Fisher-KPP type at the boundary}},
author = {Grégory Faye and Jean-Michel Roquejoffre and Mingmin Zhang},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03869},
eprint = {2609.03869},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05733457v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sharp asymptotics for a transport model with a nonlocal condition of the Fisher-KPP type at the boundary
AU - Grégory Faye
AU - Jean-Michel Roquejoffre
AU - Mingmin Zhang
PY - 2026
DA - 2026/09/01
PB - HAL
DO - 10.48550/arxiv.2609.03869
UR - https://hal.science/hal-05733457v1
AB - This paper is concerned with the precise asymptotics, as time goes to infinity, of a transport problem in a half plane coupled with a nonlinear nonlocal boundary condition. This system arises from a class of models for the spatial spread of epdemics, its space independent version being the classical Kermack-McKendrick model. Using ideas pertaining to the study of nonlocal equations of the Fisher-KPP type, and exploiting the particular structure of the model, we prove that any initially localized solution will lag behind the minimal traveling wave, with a delay that grows logarithmically in time.
ER -