An inverse problem for the heat equation
- Autores: Amin Boumenir, Vu Kim Tuan
- Localización: Proceedings of the American Mathematical Society, ISSN 0002-9939, Vol. 138, Nº 11, 2010, págs. 3911-3921
- Idioma: inglés
- DOI: 10.1090/s0002-9939-2010-10297-6
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Resumen
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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