An inverse problem for the heat equation

Boumenir, Amin; Tuan, Vu

doi:10.1090/S0002-9939-2010-10297-6

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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