Geodesic
Identifiability for Linearized Sine-Gordon Equation
J. Ha1 ; S. Gutman2
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
Mathematical modelling of natural phenomena, Tome 8 (2013) no. 1, pp. 106-121

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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.
DOI : 10.1051/mmnp/20138107

J. Ha 1 ; S. Gutman 2

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 
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J. Ha; S. Gutman. Identifiability for Linearized Sine-Gordon Equation. Mathematical modelling of natural phenomena, Tome 8 (2013) no. 1, pp. 106-121. doi: 10.1051/mmnp/20138107

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