论文标题
KPP反应扩散方程的虚拟线性
Virtual Linearity for KPP Reaction-Diffusion Equations
论文作者
论文摘要
我们表明，与KPP反应的一般反应 - 接地扩散方程的长时间解决方案在以下意义上实际上是线性的。它的领先顺序仅通过$ u = 0 $的线性化仅通过其线性化来取决于非线性反应，并且也可以通过求解PDE来恢复通用初始数据，而求解了对初始条件的限制到$ \ bbr^d $上单位立方体的限制（后者意味着这些限制性解决方案的非线性相互作用仅对整体溶液的较低级别效应）。该结果在对流系数的统一结合下保持，我们表明这很清晰。我们还将其扩展到具有非本地扩散和KPP反应的模型。
We show that long time solution dynamic for general reaction-advection-diffusion equations with KPP reactions is virtually linear in the following sense. Its leading order depends on the non-linear reaction only through its linearization at $u=0$, and it can also be recovered for general initial data by instead solving the PDE for restrictions of the initial condition to unit cubes on $\bbR^d$ (the latter means that non-linear interaction of these restricted solutions has only lower order effects on the overall solution dynamic). The result holds under a uniform bound on the advection coefficient, which we show to be sharp. We also extend it to models with non-local diffusion and KPP reactions.
