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arXiv · 2608.12379

Asymptotic Behavior and Error Bounds for Fisher-KPP Equations on the Real Half-Line

Chu Chu·M. W. Wong
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Abstract

We study the Fisher--KPP equation on the half-line under Dirichlet,Neumann, and Robin boundary conditions. For the autonomous logistic equation, we identify bounded stationary profiles converging to $1$ and obtain exponential far-field comparison estimates. We prove local uniform convergence of nontrivial Neumann solutions to $1$. Assuming local uniform convergence of the Robin solution to its stationary profile, we derive asymptotic Neumann--Robin comparison estimates. We then consider small time-periodic Neumann and Robin boundary forcing. Under exponential stability of the homogeneous linearized semigroup, we construct a locally unique small periodic lifted mild solution and obtain a first-order expansion with a uniform $O(\varepsilon^2)$ remainder in $C_0([0,\infty))$.

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Chu Chu, M. W. Wong. 2026-08-14. Asymptotic Behavior and Error Bounds for Fisher-KPP Equations on the Real Half-Line. https://arxiv.org/abs/2608.12379

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