Stability of continuation and obstacle problems in acoustic and electromagnetic scattering
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Issue Date
2010-12
Authors
Subbarayappa, Deepak Aralumallige
Advisor
Isakov, Victor
Citation
Abstract
Study 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.
Table of Content
Description
Thesis (Ph.D.)--Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics and Statistics