Parameter identifiability for heat conduction with a boundary input

Semion Gutman and Junhong Ha

Mathematics and Computers in Simulation (MATCOM), 2009, vol. 79, issue 7, 2192-2210

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.

Keywords: Identification; Identifiability; Piecewise constant conductivity (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:79:y:2009:i:7:p:2192-2210

DOI: 10.1016/j.matcom.2008.12.002

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