受控线性Schrdinger方程的温和解  

The mild solution of control linear schrdinger equations

作　　者：陶娟[1] 彭云飞[1] 项筱玲[1] 

机构地区：[1]贵州大学理学院数学系,贵州贵阳550025

出　　处：《贵州大学学报（自然科学版）》2007年第2期120-124,共5页Journal of Guizhou University:Natural Sciences

基　　金：贵州省省长基金资助

摘　　要：用Fourier变换,得到在有界区域上iΔ所生成的半群表达式,并用它引进了受控Schrdinger方程的温和解,证明了解的存在唯一性及解对初值和控制的连续依赖性。为Schrdinger方程的最优控制问题的研究打下了基础。the formula of semi-group, which generated by i△, is obtained by using the Fourier transformation. The existence and uniqueness of systems governed by the control linear Schroedinger equations are presented. And we also prove that the mild solution continuously depend on the initial value and the control. This lays foundation of the optimal control problem of linear Schroedinger equations.

关 键 词：Sehroedinger方程 温和解 半群 FOURIER变换 

分 类 号：O175.2[理学—数学]