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Partial Differential Equations Commons™

Open Access. Powered by Scholars. Published by Universities.®

1998

Articles 1 - 3 of 3

Full-Text Articles in Partial Differential Equations

Uniqueness For A Boundary Identification Problem In Thermal Imaging, Kurt Bryan, Lester Caudill Nov 1998

Uniqueness For A Boundary Identification Problem In Thermal Imaging, Kurt Bryan, Lester Caudill

Department of Math & Statistics Faculty Publications

An inverse problem for an initial-boundary value problem is considered. The goal is to determine an unknown portion of the boundary of a region in ℝn from measurements of Cauchy data on a known portion of the boundary. The dynamics in the interior of the region are governed by a differential operator of parabolic type. Utilizing a unique continuation result for evolution operators, along with the method of eigenfunction expansions, it is shown that uniqueness holds for a large and physically reasonable class of Cauchy data pairs.

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Stability And Reconstruction For An Inverse Problem For The Heat Equations, Kurt M. Bryan, Lester Caudill May 1998

Stability And Reconstruction For An Inverse Problem For The Heat Equations, Kurt M. Bryan, Lester Caudill

Mathematical Sciences Technical Reports (MSTR)

We examine the inverse problem of determining the shape of some unknown portion of the boundary of a region W from measurements of the Cauchy data for solutions to the heat equation on W. By suitably linearizing the inverse problem we obtain uniqueness and continuous dependence results. We propose an algorithm for recovering estimates of the unknown portion of the surface and use the insight gained from a detailed analysis of the inverse problem to regularize the inversion. Several computational examples are presented.

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Positive Solutions For A Concave Semipositone Dirichlet Problem, Alfonso Castro, Ratnasingham Shivaji Jan 1998

Positive Solutions For A Concave Semipositone Dirichlet Problem, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

No abstract provided for this article

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