Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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OPTIMAL PARAMETERS FOR A DAMPED SINE-GORDON EQUATION

  • Ha, Jun-Hong (SCHOOL OF LIBERAL ARTS KOREA UNIVERSITY OF TECHNOLOGY AND EDUCATION) ;
  • Gutman, Semion (DEPARTMENT OF MATHEMATICS UNIVERSITY OF OKLAHOMA)
  • Published : 2009.09.01
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Abstract

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.

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References

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  2. Identification problem for damped sine-Gordon equation with point sources vol.375, pp.2, 2011, https://doi.org/10.1016/j.jmaa.2010.10.006
  3. Identifiability for Linearized Sine-Gordon Equation vol.8, pp.1, 2013, https://doi.org/10.1051/mmnp/20138107