Some uniqueness results of discontinuous coefficients for the one-dimensional inverse spectral problem

被引:5
|
作者
Sini, M [1 ]
机构
[1] CMI, F-13453 Marseille, France
关键词
D O I
10.1088/0266-5611/19/4/306
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we deal with the inverse spectral problem for the equation -(pu')'+qu = lambdaru on a finite interval (0, h). The above equation subjected to appropriate boundary conditions on zero and h gives the vibrations of a string of length h. Using the Dirichlet-to-Neumann map type approach known in the multidimensional Calderon problem, we prove some uniqueness results of one or two discontinuous coefficients among p, q and r, and the length h from the vibrations of the end point zero. We also consider Sturm-Liouville systems of the form -(Pu')' + Qu = lambdaRu where P and R are diagonal n x n matrices and Q a symmetric n x n matrix with Linfinity (Omega) entries. In the case n = 2, this problem models the small vibrations of two connected beams. We prove the uniqueness of the matrix of rigidity P or matrix density R when its entries are piecewise constant functions.
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页码:871 / 894
页数:24
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