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INVERSE PROBLEM FOR A HEAT EQUATION WITH PIECEWISE-CONSTANT CONDUCTIVITY  

Gutman, S. (Department of Mathematics, University of Oklahoma)
Ramm, A.G. (Department of Mathematics, Kansas State University)
Publication Information
Journal of applied mathematics & informatics / v.28, no.3_4, 2010 , pp. 651-661 More about this Journal
Abstract
We consider the inverse problem of the identification of a piecewise-constant conductivity in a bar given the extra information of the heat flux through one end of the bar. Our theoretical results show that such an identification is unique. This approach utilizes a "layer peeling" argument. A computational algorithm based on this method is proposed and implemented. The advantage of this algorithm is that it requires only 3D minimizations irrespective of the number of the unknown discontinuities. Its numerical effectiveness is investigated for several conductivities.
Keywords
Identification; heat conduction; piecewise-constant conductivity; inverse problems;
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