Mathematics – Analysis of PDEs
Scientific paper
2010-03-04
Inverse Problems 26 (2010) 095004
Mathematics
Analysis of PDEs
17pages, submitted January 19, 2010
Scientific paper
10.1088/0266-5611/26/9/095004
The enclosure method was originally introduced for inverse problems of concerning non destructive evaluation governed by elliptic equations. It was developed as one of useful approach in inverse problems and applied for various equations. In this article, an application of the enclosure method to an inverse initial boundary value problem for a parabolic equation with a discontinuous coefficients is given. A simple method to extract the depth of unknown inclusions in a heat conductive body from a single set of the temperature and heat flux on the boundary observed over a finite time interval is introduced. Other related results with infinitely many data are also reported. One of them gives the minimum radius of the open ball centered at a given point that contains the inclusions. The formula for the minimum radius is newly discovered.
IKehata Masaru
Kawashita Mishio
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