Inverse Uniqueness in Interior Transmission Problem and Its Eigenvalue Tunneling in Simple Domain
Keyword(s):
We study inverse uniqueness with a knowledge of spectral data of an interior transmission problem in a penetrable simple domain. We expand the solution in a series of one-dimensional problems in the far-fields. We define an ODE by restricting the PDE along a fixed scattered direction. Accordingly, we obtain a Sturm-Liouville problem for each scattered direction. There exists the correspondence between the ODE spectrum and the PDE spectrum. We deduce the inverse uniqueness on the index of refraction from the discussion on the uniqueness anglewise of the Strum-Liouville problem.
Keyword(s):
2001 ◽
Vol 131
(6)
◽
pp. 1357-1370
1987 ◽
Vol 414
(1846)
◽
pp. 255-269
◽
2006 ◽
Vol 11
(1)
◽
pp. 47-78
◽
2014 ◽
Vol 19
(3)
◽
pp. 301-334
◽
2014 ◽
Vol 284
(01)
◽
pp. 157-162