In this paper we examine the inverse problem of determining the amount of corrosion/disbonding which has occurred on the boundary of a single circular (or nearly circular) inclusion D in a two-dimensional domain Omega , using Cauchy data for the steady-state heat equation. We develop an algorithm for reconstructing a function which quantifies the level of corrosion/disbonding at each point on the boundary of D. We also address the issue of ill-posedness and develop a simple regularization scheme, then provide several numerical examples. We also show a simple procedure for recovering the center of D assuming that Omega and D have the same thermal conductivity.

Author Bio

Nicholas Christian is a senior at the University of North Carolina at Asheville. He will be graduating in May 2005 with a Bachelor of Arts in Mathematics and a minor in Computer Science. Outside of school, Nicholas enjoys running and Pittsburgh Steelers football. This article is from reseach done while attending an REU program at the Rose-Hulman Institute of Technology, summer 2004.

Mathew Johnson is a senior mathematics major at Ball State University. He worked on this project during the summer of 2004 under the supervision of Dr. Kurt Bryan as part of the summer REU program at Rose-Hulman Institute of Technology. In the fall, he will attend University of Illinois at Urbana-Champaign and hopes to earn a Ph.D. in mathematics.