KPP fronts in a one-dimensional random drift
KPP fronts in a one-dimensional random drift
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KPP 前沿处于一维随机漂移中
DOI：
10.3934/dcdsb.2009.11.421
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发表时间：
2008
影响因子：
1.2
通讯作者：
J. Xin
中科院分区：
文献类型：
--
作者：
J. Nolen;J. Xin
我们建立了在一维随机漂移中柯尔莫哥洛夫 - 彼得罗夫斯基 - 皮斯库诺夫（KPP）前沿速度的变分原理，该随机漂移是一个具有混合性质和局部利普希茨连续性的均值为零的平稳遍历过程。为了证明变分原理，我们使用解的路径积分表示、相关随机流的首次击中时间以及大偏差估计。变分原理使我们能够推导出前沿速度的上下界，在漂移的均方根大振幅极限下，这些边界按照幂律衰减。这种标度律不同于有效扩散（均匀化）近似的标度律，后者对不可压缩周期性平流中的前沿速度是有效的。
We establish the variational principle of
Kolmogorov-Petrovsky-Piskunov (KPP) front speeds
in a one dimensional random drift which is a mean zero stationary
ergodic process with mixing property and local Lipschitz continuity.
To prove the variational principle, we use the path
integral representation of solutions,
hitting time and large deviation estimates of the
associated stochastic flows.
The variational principle allows us to derive upper and lower bounds of the
front speeds which decay according to a power law in the limit of large root mean
square amplitude of the drift. This scaling law is different from
that of the effective diffusion (homogenization) approximation
which is valid for front speeds in incompressible periodic advection.