Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation

dc.contributor.authorMilne, Tristanen
dc.contributor.departmentMathematics and Statisticsen
dc.contributor.supervisorMansouri, Abdol-Rezaen
dc.date2016-08-23 15:00:13.283
dc.date.accessioned2016-08-23T22:51:36Z
dc.date.available2016-08-23T22:51:36Z
dc.date.issued2016-08-23
dc.degree.grantorQueen's University at Kingstonen
dc.descriptionThesis (Master, Mathematics & Statistics) -- Queen's University, 2016-08-23 15:00:13.283en
dc.description.abstractWe study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an observer on the boundary of the manifold when the manifold is set into motion through boundary vibrations. We study the Dirichlet to Neumann operator when vibrations are imposed and data recorded on disjoint sets, a useful setting for applications. We prove that this operator determines the Dirichlet to Neumann operator where sources and observations are on the same set, provided a spectral condition on the Laplace-Beltrami operator for the manifold is satisfied. We prove this by providing an implementable procedure for determining a portion of the Riemannian manifold near the area where sources are applied. Drawing on established results, an immediate corollary is that a compact Riemannian manifold can be reconstructed from the Dirichlet to Neumann operator where sources and observations are on disjoint sets.en
dc.description.degreeM.Sc.en
dc.identifier.urihttp://hdl.handle.net/1974/14738
dc.language.isoengen
dc.relation.ispartofseriesCanadian thesesen
dc.rightsQueen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canadaen
dc.rightsProQuest PhD and Master's Theses International Dissemination Agreementen
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dc.rightsCopying and Preserving Your Thesisen
dc.rightsThis publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.en
dc.subjectPartial Differential Equationsen
dc.subjectInverse Problemsen
dc.titleCodomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equationen
dc.typethesisen
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