Reconstruction of the wave speed from transmission eigenvalues for the spherically symmetric variable-speed wave equation
Reconstruction of the wave speed from transmission eigenvalues for the spherically symmetric variable-speed wave equation
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DOI：
10.1088/0266-5611/29/6/065007
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发表时间：
2013-04
期刊：
影响因子：
2.1
通讯作者：
T. Aktosun;V. Papanicolaou
中科院分区：
文献类型：
--
作者：
T. Aktosun;V. Papanicolaou
在半径为B的有界球面区域中，考虑了从相应的透射本征值集合中唯一地重构球对称波速v，其中相应的本征函数也是球对称的。如果1/v在区间[0，B]上的积分小于B，假设存在至少一个对应于该数据的v，则从由这样的传输本征值及其“多重性”组成的数据唯一地重构v，其中多重性被定义为作为关键量的零的传输本征值的多重性。当该积分等于B时，当数据集包含一条附加信息时，呈现唯一重建。对于一个相关的薛定谔方程，从具有多重性的透射本征值唯一地重构出势，给出了一些类似的结果。
The unique reconstruction of a spherically symmetric wave speed v is considered in a bounded spherical region of radius b from the set of corresponding transmission eigenvalues for which the corresponding eigenfunctions are also spherically symmetric. If the integral of 1/v on the interval [0, b] is less than b, assuming that there exists at least one v corresponding to the data, then v is uniquely reconstructed from the data consisting of such transmission eigenvalues and their ‘multiplicities’, where the multiplicity is defined as the multiplicity of the transmission eigenvalue as a zero of a key quantity. When that integral is equal to b, the unique reconstruction is presented when the data set contains one additional piece of information. Some similar results are presented for the unique reconstruction of the potential from the transmission eigenvalues with multiplicities for a related Schrödinger equation.