实半直线上Fisher-KPP方程的渐近行为与误差界

中文摘要 AI 辅助

我们研究半直线上带有Dirichlet、Neumann和Robin边界条件的Fisher-KPP方程。针对自治Logistic方程，我们识别出收敛到1的有界稳态剖面，并得到指数远场比较估计。我们证明非平凡Neumann解局部一致收敛到1。假设Robin解局部一致收敛到其稳态剖面，我们推导渐近Neumann-Robin比较估计。随后考虑小时间周期Neumann和Robin边界驱动，在齐次线性化半群指数稳定的条件下，我们构造出局部唯一的小周期提升温和解，并得到在C₀([0,∞))中具有一致O(ε²)余项的一阶展开式。

英文摘要

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 $C_0([0,\infty))$.

发表机构

• York University（约克大学）

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