對三維球對稱折射率的內傳導特徵值研究

A Study of Interior Transmission Eigenvalues of the Spherically-symmetric Index of Refraction in R3

賴君旻(CHUN-MIN LAI)

指導教授 ： 陳隆暉

國立中正大學/理學院/數學系研究所/碩士(2016年)

摘要

這裡的反問題分析是在半徑為b的三維球型空間內
假設其特徵函數亦為球對稱
從相關的特徵值集合
重建球對稱波方程的波速υ

若1/υ在[0, b]的積分小於b
假設存在的情況下
經由特徵值集合
證明波速υ可被唯一決定

關鍵字

內傳導特徵值 ； 頻譜反問題分析 ； 變動速度波方程

並列摘要

Abstract
The inverse problem here is the recovery of a spherically -symmetric wave
speed υ considered in a bounded spherical region of radius b from the set of
the corresponding transmission eigenvalues for which the corresponding eigenfunctions
are also spherically symmetric. If the integral of 1/υ on the interval
[0, b] is less than b, assuming that there exists at least one υ corresponding to
the data, it is shown that υ is uniquely determined by the data consisting of
such transmission eigenvalues and their multiplicities, where the multiplicity is
defined as the multiplicity of the transmission eigenvalues as a zero of a key
quantity.

並列關鍵字

transmission eigenvalues ； inverse spectral problem ； variable speed wave equation

參考文獻

[1] L. V. Ahlfors, Complex analysis, 3rd ed., McGraw-Hill, New York,

[2] V. Barcilon, Explicit solution of the inverse problem for a vibrating

string, J. Math. Anal. Appl. 93, 224-234 (1983).

[3] F. Cakoni, M. C¸ ay¨oren, and D. Colton, Transmission eigenvalues

and the nondestructive testing of dielectrics, Inverse Problems 24,