The uniqueness in the inverse problem for transmission eigenvalues for the spherically symmetric variable-speed wave equation

Aktosun, T; Gintides, D; Papanicolaou, VG

dc.contributor.author	Aktosun, T	en
dc.contributor.author	Gintides, D	en
dc.contributor.author	Papanicolaou, VG	en
dc.date.accessioned	2014-03-01T01:37:28Z
dc.date.available	2014-03-01T01:37:28Z
dc.date.issued	2011	en
dc.identifier.issn	0266-5611	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/21505
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Physics, Mathematical	en
dc.subject.other	Dinger equation	en
dc.subject.other	Eigen-value	en
dc.subject.other	Eigenvalues	en
dc.subject.other	Variable speed	en
dc.subject.other	Wave speed	en
dc.subject.other	Inverse problems	en
dc.subject.other	Eigenvalues and eigenfunctions	en
dc.title	The uniqueness in the inverse problem for transmission eigenvalues for the spherically symmetric variable-speed wave equation	en
heal.type	journalArticle	en
heal.identifier.primary	10.1088/0266-5611/27/11/115004	en
heal.identifier.secondary	http://dx.doi.org/10.1088/0266-5611/27/11/115004	en
heal.identifier.secondary	115004	en
heal.language	English	en
heal.publicationDate	2011	en
heal.abstract	The recovery of a spherically symmetric wave speed v is 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/v on the interval [0, b] is less than b, assuming that there exists at least one v corresponding to the data, it is shown that v 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 eigenvalue as a zero of a key quantity. When that integral is equal to b, the unique recovery is obtained when the data contain one additional piece of information. Some similar results are presented for the unique determination of the potential from the transmission eigenvalues with multiplicities for a related Schrödinger equation. © 2011 IOP Publishing Ltd.	en
heal.publisher	IOP PUBLISHING LTD	en
heal.journalName	Inverse Problems	en
dc.identifier.doi	10.1088/0266-5611/27/11/115004	en
dc.identifier.isi	ISI:000296589200005	en
dc.identifier.volume	27	en
dc.identifier.issue	11	en