| Issue |
Math. Model. Nat. Phenom.
Volume 8, Number 1, 2013
Harmonic analysis
|
|
|---|---|---|
| Page(s) | 106 - 121 | |
| DOI | https://doi.org/10.1051/mmnp/20138107 | |
| Published online | 28 January 2013 | |
Identifiability for Linearized Sine-Gordon Equation
1 School of Liberal Arts, Korea
University of Technology and Education
Cheonan
330-708, South
Korea
2 Department of Mathematics, University
of Oklahoma Norman, Oklahoma
73019,
USA
∗ Corresponding author. E-mail: sgutman@ou.edu
The paper presents theoretical and numerical results on the identifiability, i.e. the unique identification for the one-dimensional sine-Gordon equation. The identifiability for nonlinear sine-Gordon equation remains an open question. In this paper we establish the identifiability for a linearized sine-Gordon problem. Our method consists of a careful analysis of the Laplace and Fourier transforms of the observation of the system, conducted at a single point. Numerical results based on the best fit to data method confirm that the identification is unique for a wide choice of initial approximations for the sought test parameters. Numerical results compare the identification for the nonlinear and the linearized problems.
Mathematics Subject Classification: 35R30 / 93B30
Key words: Identification / identifiability / sine-Gordon equation
© EDP Sciences, 2013
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