AI 中文总结
本文研究周期介质中反应-扩散-平流方程的解，证明了传播集合的存在性及传播速度的变分公式，并利用回缩解估计无界初始支撑解的上水平集位置，适用于Fisher-KPP、点火和双稳态反应。
AI 中文摘要
我们考虑全空间R^N中具有一般无界初始支撑的空间周期反应-扩散-平流方程的解。我们证明了在大时间下解的传播集合的存在性，以及传播速度的变分公式。具有无界初始支撑的解的上水平集的位置，可根据该初始支撑和具有有界初始支撑的解的传播集合来估计。这些结果适用于标准的Fisher-KPP、点火或双稳态反应类。一般结果适用于V形和Lambda形初始支撑的情形。证明特别依赖于我们称之为回缩解的上估计。
英文摘要
We consider solutions of space-periodic reaction-diffusion-advection equations in the whole space R^N, with general unbounded initial support. We show the existence of spreading sets for the solutions at large time, and variational formulas for the spreading speeds. The location of the upper-level sets of a solution with unbounded initial support is estimated in terms of that initial support and the spreading set for the solutions with bounded initial supports. The results hold for the standard classes of Fisher-KPP, ignition, or bistable reactions. The general results apply to the cases of V-shaped and Lambda-shaped initial supports. The proofs rely in particular on upper estimates of what we call retracting solutions.
