An inverse problem for the heat equation
Open Access
- 1 July 2010
- journal article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 138 (11) , 3911-3921
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.Keywords
This publication has 15 references indexed in Scilit:
- Computing Sturm–Liouville potentials from two spectraInverse Problems, 2006
- Determining the potential in the Schrödinger equation from the Dirichlet to Neumann map by the boundary control methodJournal of Inverse and Ill-posed Problems, 2005
- Solving Inverse Problems with Spectral Data2000
- The recovery of analytic potentialsInverse Problems, 1999
- The BC-method in the inverse problem for the heat equationJournal of Inverse and Ill-posed Problems, 1997
- The determination of a coefficient in a parabolic equation from input sourcesIMA Journal of Applied Mathematics, 1994
- On uniqueness in inverse problems for semilinear parabolic equationsArchive for Rational Mechanics and Analysis, 1993
- The Recovery of Potentials from Finite Spectral DataSIAM Journal on Mathematical Analysis, 1992
- Analytical Methods for Recovering Coefficients in Differential Equations from Spectral DataSIAM Review, 1986
- DETERMINATION OF A DIFFERENTIAL EQUATION BY TWO OF ITS SPECTRARussian Mathematical Surveys, 1964