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arXiv · 2609.03869

Sharp asymptotics for a transport model with a nonlocal condition of the Fisher-KPP type at the boundary

Grégory Faye·Jean-Michel Roquejoffre·Mingmin Zhang
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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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Grégory Faye, Jean-Michel Roquejoffre, Mingmin Zhang. 2026-09-03. Sharp asymptotics for a transport model with a nonlocal condition of the Fisher-KPP type at the boundary. https://arxiv.org/abs/2609.03869

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