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

• Main Authors: LAI,CHUN-MIN, 賴君旻
• Other Authors: CHEN, LUNG-HUI
• Format: Others
• Language: en_US
• Published: 2016
• Online Access: http://ndltd.ncl.edu.tw/handle/94266484473978110461

碩士 === 國立中正大學 === 數學系研究所 === 104 === 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.