由内部谱数据确定的扩散算子的反问题

摘要/Abstract

摘要：

研究了有限区间[0, π] 上的扩散算子的反问题, 证明如果已知边界条件中的系数h, 则部分特征函数在(0, π) 内某点的函数值及二组谱的部分谱能够惟一确定势函数(q, p) 及边界条件中的系数H.

Abstract:

In this paper, we discuss the inverse problem for diffusion operators on the finite interval [0, π] from interior spectral data and show that if coefficient h of the boundary condition is known a priori, then the potentials (q, p) and coefficient H of the boundary condition can be uniquely determined by a set of values of eigenfunctions at some interior point and parts of two spectra.

Key words: Inverse problem, Diffusion operator, Potential, Uniqueness theorem, Eigenvalue

中图分类号:

34A55

王於平. 由内部谱数据确定的扩散算子的反问题[J]. 数学物理学报, 2013, 33(6): 1189-1195.

WANG Yu-Ping. Inverse Problem for Diffusion Operators from Interior Spectral Data[J]. Acta mathematica scientia,Series A, 2013, 33(6): 1189-1195.

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