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2011 | 9 | 2 | 269-280

Tytuł artykułu

Optimal control of nonlinear one-dimensional periodic wave equation with x-dependent coefficients

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
This paper is concerned with an optimal control problem governed by the nonlinear one dimensional periodic wave equation with x-dependent coefficients. The control of the system is realized via the outer function of the state. Such a model arises from the propagation of seismic waves in a nonisotropic medium. By investigating some important properties of the linear operator associated with the state equation, we obtain the existence and regularity of the weak solution to the state equation. Furthermore, the existence of the optimal control is proved by means of the Arzelà-Ascoli lemma and Sobolev compact imbedding theorem.

Wydawca

Czasopismo

Rocznik

Tom

9

Numer

2

Strony

269-280

Opis fizyczny

Daty

wydano
2011-04-01
online
2011-02-18

Twórcy

autor
  • Jilin University
autor
  • Jilin University

Bibliografia

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  • [3] Barbu V, Optimal control of the one-dimensional periodic wave equation, Appl. Math. Optim., 1997, 35(1), 77–90
  • [4] Barbu V, Pavel N.H., Periodic solutions to one-dimensional wave equation with piece-wise constant coefficients, J. Differential Equations, 1996, 132(2), 319–337 http://dx.doi.org/10.1006/jdeq.1996.0182
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  • [6] Barbu V., Pavel N.H., Periodic solutions to nonlinear one dimensional wave equation with x-dependent coefficients, Trans. Amer. Math. Soc, 1997, 349(5), 2035–2048 http://dx.doi.org/10.1090/S0002-9947-97-01714-5
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  • [14] Ji S., Li Y., Periodic solutions to one-dimensional wave equation with x-dependent coefficients, J. Differential Equations, 2006, 229(2), 466–493 http://dx.doi.org/10.1016/j.jde.2006.03.020
  • [15] Ji S., Li Y., Time-periodic solutions to the one-dimensional wave equation with periodic or anti-periodic boundary conditions, Proc. Roy. Soc. Edinburgh Sect. A, 2007, 137(2), 349–371 http://dx.doi.org/10.1017/S0308210505001174
  • [16] Ji S., Li Y., Time periodic solutions to one-dimensional nonlinear wave equation, Arch. Ration. Mech. Anal., DOI: 10.1007/s00205-010-0328-4
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Typ dokumentu

Bibliografia

Identyfikatory

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bwmeta1.element.doi-10_2478_s11533-010-0098-0
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