Alan Von Herrmann

Advisor: Jennifer Mueller

Degree Conferred: Summer 2009

After Graduation: Assistant Professor, Arian College

Website: http://www.adrian.edu/academics/MATH/

Thesis Title:

Properties of the Reconstruction Algorithm and Associated Scattering Transform for Admittivities in the Plane

Abstract:

We consider the inverse admittivity problem in dimension two. The focus of this dissertation is to develop some properties of the scattering transform $S_\gamma(k)$ with $\gamma\in W^{1,p}(\Omega)$ and to develop properties of the exponentially growing solutions to the admittivity equation. We consider the case when the potential matrix is Hermitian and the definition of the potential matrix used by Francini [Inverse Problems, 16, 2000].  These exponentially growing solutions play a role in developing a reconstruction algorithm from the Dirichlet-to-Neumann map of $\gamma.$ A boundary integral equation is derived relating the Dirichlet-to-Neumann map of $\gamma$ to the exponentially growing solutions to the admittivity equation.