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May 2008 Identification of Some Spatially Variable Physical Properties
A. Badran
Missouri J. Math. Sci. 20(2): 138-149 (May 2008). DOI: 10.35834/mjms/1316032814


An inverse problem for the identification of an unknown spatially dependent coefficient in a parabolic partial differential equation is considered as an application for this new technique. An integral identity which explicitly relates changes in coefficients to changes in measured data is presented. Using this identity, it is possible to show that the coefficient to data map is continuous, strictly monotone and injective. Applying a modified Backus-Gilbert method to this identity generates a sequence of coefficients converging to the required unknown coefficient. Finally, implementation of the procedure is discussed and some numerical experiments are displayed.


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A. Badran. "Identification of Some Spatially Variable Physical Properties." Missouri J. Math. Sci. 20 (2) 138 - 149, May 2008.


Published: May 2008
First available in Project Euclid: 14 September 2011

zbMATH: 1155.35107
Digital Object Identifier: 10.35834/mjms/1316032814

Primary: 00A69
Secondary: 45B05 , 65R30

Rights: Copyright © 2008 Central Missouri State University, Department of Mathematics and Computer Science


Vol.20 • No. 2 • May 2008
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