论文标题
晶格$ \ mathbb {z} $上的Fisher-kpp方程的对数Bramson校正
The logarithmic Bramson correction for Fisher-KPP equations on the lattice $\mathbb{Z}$
论文作者
论文摘要
我们在本文中建立了对数bramson校正的晶格$ \ mathbb {z} $上的Fisher-kpp方程。具有逐步初始条件的解决方案的级别集位于位置$ c_*t- \ frac {3} {2λ_*} \ ln t+\ mathcal {o}（1）$ as $ t \ rightArrow+rightArrow+\ rightArrow+\ infty $ c _*$ c _*$ c _*$ and $ c $和$ cist $ and $ c _*$ and $ c。这将Bramson在连续环境中的众所周知的结果扩展到仅使用PDE参数的离散案例。我们的分析的副产品还使解决方案接近对数的一家对数的旅行前解决方案的家族，并以最小的波速$ c _*$在正整数上均匀地转移，并且该解决方案沿着其级别的设置汇聚到大型旅行的最小行进前线。
We establish in this paper the logarithmic Bramson correction for Fisher-KPP equations on the lattice $\mathbb{Z}$. The level sets of solutions with step-like initial conditions are located at position $c_*t-\frac{3}{2λ_*}\ln t+\mathcal{O}(1)$ as $t\rightarrow+\infty$ for some explicit positive constants $c_*$ and $λ_*$. This extends a well-known result of Bramson in the continuous setting to the discrete case using only PDE arguments. A by-product of our analysis also gives that the solutions approach the family of logarithmically shifted traveling front solutions with minimal wave speed $c_*$ uniformly on the positive integers, and that the solutions converge along their level sets to the minimal traveling front for large times.
