J. Korean Math. Soc. 2010; 47(5): 1077-1095
Printed September 1, 2010
https://doi.org/10.4134/JKMS.2010.47.5.1077
Copyright © The Korean Mathematical Society.
Semion Gutman and Junhong Ha
University of Oklahoma and Korea University of Technology and Education
The paper considers the identifiability (i.e., the unique identification) of a composite string in the class of piecewise constant parameters. The 1-D string vibration is measured at finitely many observation points. The observations 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 parameters. A numerical algorithm for the identification in the presence of noise is proposed and implemented.
Keywords: identification, identifiability, piecewise constant parameters, string vibration
MSC numbers: 35R30, 93B30
1997; 34(4): 895-909
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