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1998 | 76 | 1 | 117-142
Tytuł artykułu

Exact Neumann boundary controllability for second order hyperbolic equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Using HUM, we study the problem of exact controllability with Neumann boundary conditions for second order hyperbolic equations. We prove that these systems are exactly controllable for all initial states in $L^2({\mit\Omega})\times (H^1({\mit\Omega}))'$ and we derive estimates for the control time T.
Rocznik
Tom
76
Numer
1
Strony
117-142
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-02-17
poprawiono
1997-07-18
Twórcy
autor
  • Department of Mathematics, University of Wollongong, Northfields Avenue Wollongong, New South Wales 2522, Australia
  • Department of Mathematics, University of Wollongong, Northfields Avenue Wollongong, New South Wales 2522, Australia
Bibliografia
  • [1] R. F. Apolaya, Exact controllability for temporally wave equations, Portugal. Math. 51 (1994), 475-488.
  • [2] C. Bardos, G. Lebeau and J. Rauch, Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary, SIAM J. Control Optim. 30 (1992), 1024-1065.
  • [3] R. Dautray and J. L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 5, Evolution Problems I, Springer, Berlin, 1992.
  • [4] J. K. Hale, Ordinary Differential Equations, Wiley-Interscience, New York, 1969.
  • [5] V. Komornik, Exact controllability in short time for the wave equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 6 (1989), 153-164.
  • [6] V. Komornik, Contrôlabilité exacte en un temps minimal, C. R. Acad. Sci. Paris Sér. I Math. 304 (1987), 223-225.
  • [7] O. A. Ladyzhenskaya, The Boundary Value Problems of Mathematical Physics, Springer, New York, 1985.
  • [8] I. Lasiecka, J. L. Lions and R. Triggiani, Nonhomogeneous boundary value problems for second order hyperbolic operators, J. Math. Pures Appl. 65 (1986), 149-192.
  • [9] J. L. Lions, Contrôlabilité exacte$,$ perturbations et stabilisation de systèmes distribués, Tome $1$, Contrôlabilité exacte, Masson, Paris, 1988.
  • [10] J. L. Lions and E. Magenes, Non-homogeneous Boundary Value Problems and Applications, Vols. I and II, Springer, Berlin, 1972.
  • [11] M. M. Miranda, HUM and the wave equation with variable coefficients, Asymptotic Anal. 11 (1995), 317-341.
  • [12] J. E. Mu noz Rivera, Exact controllability\rm: coefficient depending on the time, SIAM J. Control Optim. 28 (1990), 498-501.
  • [13] D. L. Russell, Exact boundary value controllability theorems for wave and heat processes in star-complemented regions, in: Differential Games and Control Theory, E. O. Roxin, P. T. Liu, and R. L. Sternberg (eds.), Lecture Notes in Pure Appl. Math. 10, Marcel Dekker, New York, 1974, 291-319.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv76z1p117bwm
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