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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
Bibliografia
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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
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-010-0098-0
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