Parameter identifiability for heat conduction with a boundary input

Authors:
Semion Gutman;Junhong Ha
Affiliations:
Department of Mathematics, University of Oklahoma, Norman, OK 73019, USA;School of Liberal Arts, Korea University of Technology and Education, Cheonan 330-708, South Korea
Venue:
Mathematics and Computers in Simulation
Year:
2009

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Abstract

The identifiability (i.e. the unique identification) of conductivity in a heat conduction process is considered in the class of piecewise constant conductivities. The 1-D process may have nonzero boundary inputs as well as distributed inputs. Its measurements are collected at finitely many observation points. They are processed to obtain the first eigenvalue and a constant multiple of the first eigenfunction at the observation points. It is shown that the identification by the Marching Algorithm is continuous with respect to the mean convergence in the admissible set. The result is based on the continuous dependence of eigenvalues, eigenfunctions, and the solutions on the conductivities. Numerical experiments confirm the perfect identification for noiseless data. A numerical algorithm for the identification in the presence of noise is proposed and implemented.