具有阻尼波方程与Schrdinger耦合系统的Legendre谱分析  

Legendre Spectral Analysis to a Schrdinger Equation Coupled with a Damped Wave Equation

作　　者：熊梦清 王军民[1] 

机构地区：[1]北京理工大学数学与统计学院,北京100081

出　　处：《应用泛函分析学报》2017年第1期80-87,共8页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(61673061)

摘　　要：运用Legendre谱方法研究Schrdinger方程与具有黏性阻尼波方程耦合组成的系统稳定性问题.首先通过分析得到耦合系统能量不增长,再利用Legendre谱方法对该系统特征方程进行数值化,并利用MATLAB计算得到该耦合系统的谱分布,从而根据系统特征根全部分布在复平面的左半平面并距离虚轴一定距离得到该耦合系统达到了强稳定.最后将Legendre谱方法应用到热方程与Schrdinger耦合系统的稳定性.An Legendre spectral method is used to study the stability of a SchrSdinger equation coupled with a damped wave equation which acts a dynamic controller for the SchrSdinger equation. The graphic numerical solutions are presented. Remarkably, the spectrum generated by the closed-loop system is distributed into the left half-plane of the complex plane, which notes that the system is dissipative. Combining the energy of the system is not increasing, we can see the coupled system achieves the strong stability. At last, the Legendre spectral method is also used to verify the stability of a SchrSdinger system coupled with a heat equation.

关 键 词：SCHRODINGER方程 波方程 LEGENDRE谱方法 稳定性 

分 类 号：O231.4[理学—运筹学与控制论]