Eigenvalue asymptotics of layered media and their applications to the inverse problem

Athanassoulis, GA; Papanicolaou, VG

dc.contributor.author	Athanassoulis, GA	en
dc.contributor.author	Papanicolaou, VG	en
dc.date.accessioned	2014-03-01T01:12:49Z
dc.date.available	2014-03-01T01:12:49Z
dc.date.issued	1997	en
dc.identifier.issn	0036-1399	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/12256
dc.subject	Eigenvalue asymptotics	en
dc.subject	Layered medium	en
dc.subject	Piecewise smooth potential	en
dc.subject	Reconstruction of jumps	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Acoustics	en
dc.subject.other	Boundary conditions	en
dc.subject.other	Differentiation (calculus)	en
dc.subject.other	Eigenvalues and eigenfunctions	en
dc.subject.other	Inverse problems	en
dc.subject.other	Mathematical models	en
dc.subject.other	Partial differential equations	en
dc.subject.other	Problem solving	en
dc.subject.other	Refractive index	en
dc.subject.other	Classical Sturm-Liouville problem	en
dc.subject.other	Eigenvalue asymptotics	en
dc.subject.other	Jump discontinuities	en
dc.subject.other	Layered media	en
dc.subject.other	Piecewise smooth coefficients	en
dc.subject.other	Wave propagation	en
dc.title	Eigenvalue asymptotics of layered media and their applications to the inverse problem	en
heal.type	journalArticle	en
heal.identifier.primary	10.1137/S0036139995283602	en
heal.identifier.secondary	http://dx.doi.org/10.1137/S0036139995283602	en
heal.language	English	en
heal.publicationDate	1997	en
heal.abstract	We compute the asymptotics of the eigenvalues of the classical Sturm-Liouville problem with a piecewise smooth coefficient q. This means that q and/or its derivatives can have jump discontinuities. The boundary conditions are arbitrary. Our results extend the classical work of H. Hochstadt (see [Comm. Pure Appl. Math., 14 (1961), pp. 749-764]) and some related formulas discovered by G. Borg (see [Acta Math., 78 (1946), pp. 1-96]). Then, we apply our results to the inverse problem of determining the interfaces in a layered medium from acoustic data, since the index of refraction of such a medium can be considered piecewise smooth.	en
heal.publisher	SIAM PUBLICATIONS	en
heal.journalName	SIAM Journal on Applied Mathematics	en
dc.identifier.doi	10.1137/S0036139995283602	en
dc.identifier.isi	ISI:A1997WR38800008	en
dc.identifier.volume	57	en
dc.identifier.issue	2	en
dc.identifier.spage	453	en
dc.identifier.epage	471	en