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An inverse problem for the heat equation
Author(s):
Amin
Boumenir;
Vu
Kim
Tuan
Journal:
Proc. Amer. Math. Soc.
138
(2010),
3911-3921.
MSC (2010):
Primary 35R30, 34K29
Posted:
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:
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
Posted:
July 1, 2010
Communicated by:
Peter A. Clarkson
Copyright of article:
Copyright
2010,
American Mathematical Society
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