非线性发展方程的初值随机化问题研究

Initial value randomization of nonlinear evolution equations

主要介绍一些非线性发展方程的初值随机化问题.首先给出了薛定谔方程的初值随机化问题,KdV方程的初值随机化问题,波动方程的初值随机化问题;接着,给出了初值随机化所用到的调和分析工具;最后,提出了一些非线性发展方程在初值随机化方面未解决的问题.

This paper aims to introduce some nonlinear evolution equations.Firstly,we presents Schrodinger equtaions with random data,KdV equation with random data,wave equation with random data.Then this paper gives the harmonic analysis tools which are used to solve random data problem.At last,some unsolved problems related to random data were presented.