基于混合谱数据的不连续Sturm-Liouville逆谱问题局部可解性和稳定性  

Local Solvability and Stability of the Inverse Spectral Problems for the Discontinuous Sturm-Liouville Problem with the Mixed Given Data

作　　者：郭燕 徐小川 Guo Yan;Xu Xiaochuan(School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044;Center for Applied Mathematics of Jiangsu Province,Nanjing University of Information Science and Technology,Nanjing 210044;Jiangsu International Joint Laboratory on System Modeling and Data Analysis,Nanjing University of Information Science and Technology,Nanjing 210044)

机构地区：[1]南京信息工程大学数学与统计学院,南京210044 [2]南京信息工程大学江苏省应用数学中心,南京210044 [3]南京信息工程大学江苏省系统建模与数据分析国际合作联合实验室,南京210044

出　　处：《数学物理学报（A辑）》2024年第4期859-870,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金(11901304)。

摘　　要：该文研究有限区间(0,1)上具有Robin边界条件和不连续点x=d∈(0,12]的Sturm-Liouville算子逆谱问题.假设已知的数据为一组子谱、势函数在(d,1)上的信息以及右边界条件和不连续条件中的部分参数,该文证明恢复(0,d)上的势函数和左边界条件参数的逆谱问题局部可解性和稳定性,其中已知的势函数信息和右边界条件参数允许存在一定的误差.This paper studies inverse spectral problems for the Sturm-Liouville operator on(0,1)with the Robin boundary conditions and a discontinuity at x=d∈(0,12].Suppose that the known data contains one subspectrum,the potential function on(d,1)as well as partial parameters in the right boundary condition and the discontinuous conditions.The paper proves the local solvability and stability for the inverse problems of recovering the potential function on(0,d)and the parameter in left boundary condition,where the known potential and the parameter in the right boundary condition are allowed to contain errors.

关 键 词：STURM-LIOUVILLE算子 不连续条件 局部可解性 稳定性 

分 类 号：O175.7[理学—数学]