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OPTIMAL PARAMETERS FOR A DAMPED SINE-GORDON EQUATION
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 Title & Authors
OPTIMAL PARAMETERS FOR A DAMPED SINE-GORDON EQUATION
Ha, Jun-Hong; Gutman, Semion;
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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.
 Keywords
optimal control;necessary condition;bang-bang control law;
 Language
English
 Cited by
1.
Identifiability for Linearized Sine-Gordon Equation, Mathematical Modelling of Natural Phenomena, 2013, 8, 1, 106  crossref(new windwow)
2.
Identification problem for damped sine-Gordon equation with point sources, Journal of Mathematical Analysis and Applications, 2011, 375, 2, 648  crossref(new windwow)
3.
Fréchet differentiability for a damped sine-Gordon equation, Journal of Mathematical Analysis and Applications, 2009, 360, 2, 503  crossref(new windwow)
 References
1.
A. R. Bishop, K. Fesser, and P. S. Lomdahl, Influence of solitons in the initial state on chaos in the driven damped sine-Gordon system, Phys. D 7 (1983), no. 1-3, 259–279 crossref(new window)

2.
R. Dautary and J. L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 5, Evolution Problems I, Springer-Verlag, 1992

3.
S. Gutman, Identification of piecewise-constant potentials by fixed-energy phase shifts, Appl. Math. Optim. 44 (2001), no. 1, 49–65 crossref(new window)

4.
J. Ha and S. Nakagiri, Existence and regularity of weak solutions for semilinear second order evolution equations, Funkcial. Ekvac. 41 (1998), no. 1, 1–24

5.
J. Ha and S. Nakagiri, Identification problems of damped sine-Gordon equations with constant parameters, J. Korean Math. Soc. 39 (2002), no. 4, 509.524 crossref(new window)

6.
J. Ha and S. Nakagiri, Identification problems for the system governed by abstract nonlinear damped second order evoution equations, J. Korean Math. Soc. 41 (2004), no. 3, 435.459

7.
J. Ha and S. Nakagiri, Identification of constant parameters in perturbed sin-Gordon equations, J. Korean Math. Soc. 43 (2006), no. 5, 931.950 crossref(new window)

8.
M. Levi, Beating modes in the Josephson junction, Chaos in nonlinear dynamical systems (Research Triangle Park, N.C., 1984), 56.73, SIAM, Philadelphia, PA, 1984

9.
B. Mercier, An Introdution to the Numerical Analysis of Spectral Methods, Lecture Notes in Physis 318, Springer-Verlag 1989

10.
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recepies in FORTRAN (2nd Ed.), Cambridge University Press, Cambridge

11.
R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, 2nd ed., Applied Mathematical Sciences, Vol. 68, Springer-Verlag, 1997