Browsing MATH Theses and Dissertations by Author "Isakov, Victor"
Now showing items 111 of 11

Crack detection in a three dimensional body
Redpath, Steven F. (200605)We propose a method of analyzing a crack in a three dimensional body. We treat the problem as an inverse problem and apply Green’s Theorem, Trace Theorem, and the Fredholm Alternative. We model the problem using Helmholtz ... 
Epileptic foci localization using the inverse source problem for Maxwell's equations
Kehler, Joshua Lee (Wichita State University, 202005)Consider an application of the inverse source problem for Maxwell's equations to the matter of epileptic foci localization in the human brain. Using a current dipole to model the epileptic focus in the brain, and by ... 
Increased stability of solutions to the Helmholtz equation
Aralumallige, Deepak (200512)Study of the Cauchy problem for Helmholtz equation is stimulated by the inverse scattering theory and more generally by remote sensing. This thesis explains the increased stability of the Cauchy problem for Helmholtz ... 
Increasing stability for the inverse scattering source problem with many frequencies
Entekhabi, Mozhgan (Nora) (Wichita State University, 201807)In mathematics and physics, the inverse scattering problem is the problem of determining characteristics of an object, based on data of how it scatters incoming radiation or particles. It is the inverse problem to the ... 
Increasing stability in the inverse problem for the Schrödinger equation
Liang, Li (Wichita State University, 201512)The Schrödinger equation is a partial differential equation that describes how the quantum state of a physical system changes with time. It was formulated in late 1925 by the Austrian physicist Erwin Schrödinger. The study ... 
Inverse doping profile analysis for semiconductor quality control
Myers, Joseph Kenneth (Wichita State University, 200912)Inverse doping pro le problems are linked to inverse conductivity problems under the assumptions of zero space charge and low injection. Unipolar inverse conductivity problems are analyzed theoretically via three uniqueness ... 
Investigations in single layer gravitational potential
Stewart, Darrell Anne (Wichita State University, 201005) 
A linearised inverse conductivity problem for the Maxwell system at a high frequency
Isakov, Victor; Lu, Shuai; Xu, Boxi (Elsevier, 20220415)We consider a linearised inverse conductivity problem for electromagnetic waves in a three dimensional bounded domain at a high timeharmonic frequency. Increasing stability bounds for the conductivity coefficient in the ... 
On the inverse gravimetry problem with minimal data
Titi, Aseel (Wichita State University, 202107)In this dissertation we considered the inverse source problem $\Delta u = \mu,$ where lim $u (x) = 0$ as x goes to $\infty$ and $\mu$ is zero outside a bounded domain $\Omega$. The inverse problem of gravime try is ... 
Stability of continuation and obstacle problems in acoustic and electromagnetic scattering
Subbarayappa, Deepak Aralumallige (Wichita State University, 201012)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 ... 
Theoretical results in inverse problems for size, solvability, and uniqueness in the pn junction and doping profile of semiconductors
Myers, Joseph Kenneth (200605)We present an overview of mathematical models for electrons and holes in semiconductors. We use these to pose some inverse problems for determining the doping profile of a semiconductor. We establish the solvability of ...