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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An inverse problem for the heat equation
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by Amin Boumenir and Vu Kim Tuan PDF
Proc. Amer. Math. Soc. 138 (2010), 3911-3921 Request permission

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
  • 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