Spectral properties of exterior transmission problem for spherically stratified anisotropic media

ABSTRACT

The exterior transmission eigenvalue problem for anisotropic media with spherical symmetry assumptions is considered. First, we discuss the existence and the asymptotic distribution of exterior transmission eigenvalues. Then, we investigate the inverse problem of determining the index of refraction from a knowledge of two sets of spectral data under appropriate conditions.

KEYWORDS:

• Inverse scattering
• exterior transmission eigenvalues
• distribution
• spectral theory
• uniqueness

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 34B24
• 78A45
• 78A46

Acknowledgements

We would like to thank the referees for a very careful reading of our manuscript and for their valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This research was supported by the National Natural Science Foundation of China (Grant No. 11601372 and No. 11601384).