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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2009; 46(5): 1105-1117

Printed September 1, 2009

https://doi.org/10.4134/JKMS.2009.46.5.1105

Copyright © The Korean Mathematical Society.

Optimal parameters for a damped sine-Gordon equation

Junhong Ha and Semion Gutman

Korea University of Technology and Education and University of Oklahoma

Abstract

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In this paper a parameter identification problem for a damped sine-Gordon equation is studied from the theoretical and numerical perspectives. A spectral method is developed for the solution of the state and the adjoint equations. The Powell's minimization method is used for the numerical parameter identification. The necessary conditions for the optimization problem are shown to yield the bang-bang control law. Numerical results are discussed and the applicability of the necessary conditions is examined.

Keywords: optimal control, necessary condition, bang-bang control law

MSC numbers: Primary 49J20, 49K20

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