分数阶薛定谔方程反演左边界的拟边界正则化方法  

The Quasi-boundary regularization method for inverting the leftboundary of fractional Schr dinger equation

作　　者：高银霞 杨帆[1] 张成 GAO Yin-xia;YANG Fan;ZHANG Cheng(School of Science,Lanzhou Univ.of Tech.,Lanzhou 730050,China)

机构地区：[1]兰州理工大学理学院,甘肃兰州730050

出　　处：《兰州理工大学学报》2024年第4期147-152,共6页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(11961044)。

摘　　要：研究无界区域上时间分数阶薛定谔方程的反演左边界反问题,这是一个不适定问题,即问题的解不连续依赖于测量数据.利用拟边界正则化方法求解此反问题,给出拟边界正则解.在先验和后验正则化参数选取规则之下给出正则解和精确解的误差估计.The problem of inverting the left boundary of the time-fractional Schr dinger equation in the unbounded region is studied,which is an ill-posed problem,meaning that the solution discontinuously depends on the measurement data.A quasi-boundary regularization method is used to solve this inverse problem,and its regularized solution is given.The error estimates between the regularization solution and the exact solution are derived under the priori and the posteriori regularization parameter selection rule.

关 键 词：时间分数阶薛定谔方程 反演左边界 不适定问题 拟边界正则化方法 

分 类 号：O175[理学—数学]