## An inverse problem for the heat equation

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- by Amin Boumenir and Vu Kim Tuan
- Proc. Amer. Math. Soc.
**138**(2010), 3911-3921 - DOI: https://doi.org/10.1090/S0002-9939-2010-10297-6
- Published electronically: July 1, 2010
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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.## References

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## Bibliographic Information

**Amin Boumenir**- Affiliation: Department of Mathematics, University of West Georgia, Carrollton, Georgia 30118
- MR Author ID: 288615
- Email: boumenir@westga.edu
**Vu Kim Tuan**- Affiliation: Department of Mathematics, University of West Georgia, Carrollton, Georgia 30118
- Email: vu@westga.edu
- Received by editor(s): October 5, 2007
- Published electronically: July 1, 2010
- Communicated by: Peter A. Clarkson
- © Copyright 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**138**(2010), 3911-3921 - MSC (2010): Primary 35R30, 34K29
- DOI: https://doi.org/10.1090/S0002-9939-2010-10297-6
- MathSciNet review: 2679613