Transport equations for a general class of evolution equations with random perturbations
Transport equations for a general class of evolution equations with random perturbations
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具有随机扰动的一般类演化方程的输运方程
DOI：
10.1063/1.533003
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发表时间：
1999
影响因子：
1.3
通讯作者：
Xiao Ping Wang
中科院分区：
文献类型：
--
作者：
Maozheng Guo;Xiao Ping Wang
本文从一类形式为iut=H（X，D）u+V（X，D）u的方程导出迁移方程，其中H（X，D）和V（X，D）分别是符号为H（x，k）和V（x，k）的伪微分算子（Weyl算子），其中H（x，k）是关于k的多项式，在x上是光滑的，V（x，k）是平均零随机函数，在空间变量上是平稳的.我们也考虑上述形式的方程组。这样的方程涵盖了波传播中出现的许多方程，例如Ryzhik、Papanicolaou和Keller的论文[Wave Motion 24，327-370（1996）]中考虑的那些方程。我们的结果推广了Ryzhik，Papanicolau和Keller的结果。
We derive transport equations from a general class of equations of form iut=H(X,D)u+V(X,D)u where H(X,D) and V(X,D) are pseudodifferential operators (Weyl operator) with symbols H(x,k) and V(x,k), where H(x,k) being polynomial in k and smooth in x,V(x,k) is a mean zero random function and is stationary in space variable. We also consider system of equations in the above form. Such equations cover many of the equations that arise in wave propagations, such as those considered in a paper by Ryzhik, Papanicolaou, and Keller [Wave Motion 24, 327–370 (1996)]. Our results generalize those by Ryzhik, Papanicolau, and Keller.