Stability of continuation and obstacle problems in acoustic and electromagnetic scattering

dc.contributor.advisorIsakov, Victor
dc.contributor.authorSubbarayappa, Deepak Aralumallige
dc.date.accessioned2011-08-19T13:55:37Z
dc.date.available2011-08-19T13:55:37Z
dc.date.copyright2010
dc.date.issued2010-12
dc.descriptionThesis (Ph.D.)--Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics and Statisticsen_US
dc.description.abstractStudy of the Cauchy problem for Helmholtz equation is motivated by the inverse scattering theory and more generally by remote sensing. In this dissertation the increased stability of the Cauchy problem for Helmholtz equation and the Maxwell's system is investigated with varying frequency. Here it has been shown that the the stability of continuation is improving with the increasing frequency. The continuation is inside the convex hull of the surface where the Cauchy data is given. This has been demonstrated by numerical experiments with simple geometry. When we continue outside of the convex hull, the subspace of stable solutions is growing with frequency. This is also demonstrated by numerical experiments where we reconstruct the density function of the single layer potential. Another problem that is presented here is the electromagnetic obstacle scattering problem, with variable frequency. Here the existence and uniqueness of the solution to the forward problem is presented and the analytic dependence of the solution on the frequency is proved.en_US
dc.format.extentx, 67 p.en
dc.identifier.otherd10020
dc.identifier.urihttp://hdl.handle.net/10057/3645
dc.language.isoen_USen_US
dc.publisherWichita State Universityen_US
dc.rightsCopyright Deepak Aralumallige Subbarayappa, 2010. All rights reserveden
dc.subject.lcshElectronic dissertationsen
dc.titleStability of continuation and obstacle problems in acoustic and electromagnetic scatteringen_US
dc.typeDissertationen_US
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