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

DOI:
https://doi.org/10.1090/S0002-9939-2010-10297-6

Published electronically:
July 1, 2010

MathSciNet review:
2679613

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-2010-10297-6

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