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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An inverse problem for the heat equation


Authors: Amin Boumenir and Vu Kim Tuan
Journal: Proc. Amer. Math. Soc. 138 (2010), 3911-3921
MSC (2010): Primary 35R30, 34K29
Published electronically: July 1, 2010
MathSciNet review: 2679613
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Abstract: We prove that we can uniquely recover the coefficient of a one dimensional heat equation from a finite set of measurements and provide a constructive procedure for its recovery. The algorithm is based on the well known Gelfand-Levitan-Gasymov inverse spectral theory of Sturm-Liouville operators. By using a hot spot, as a first initial condition, we determine nearly all except maybe a finite number of spectral data. A counting procedure helps detect the number of missing data which is then unraveled by a finite number of measurements.


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Additional Information

Amin Boumenir
Affiliation: Department of Mathematics, University of West Georgia, Carrollton, Georgia 30118
Email: boumenir@westga.edu

Vu Kim Tuan
Affiliation: Department of Mathematics, University of West Georgia, Carrollton, Georgia 30118
Email: vu@westga.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10297-6
PII: S 0002-9939(2010)10297-6
Keywords: Heat equation, inverse spectral problem
Received by editor(s): October 5, 2007
Published electronically: July 1, 2010
Communicated by: Peter A. Clarkson
Article copyright: © Copyright 2010 American Mathematical Society