Exact boundary observability for quasilinear hyperbolic systems

Tatsien Li

ESAIM: Control, Optimisation and Calculus of Variations (2008)

  • Volume: 14, Issue: 4, page 759-766
  • ISSN: 1292-8119

Abstract

top
By means of a direct and constructive method based on the theory of semi-global C1 solution, the local exact boundary observability is established for one-dimensional first order quasilinear hyperbolic systems with general nonlinear boundary conditions. An implicit duality between the exact boundary controllability and the exact boundary observability is then shown in the quasilinear case.

How to cite

top

Li, Tatsien. "Exact boundary observability for quasilinear hyperbolic systems." ESAIM: Control, Optimisation and Calculus of Variations 14.4 (2008): 759-766. <http://eudml.org/doc/250273>.

@article{Li2008,
abstract = { By means of a direct and constructive method based on the theory of semi-global C1 solution, the local exact boundary observability is established for one-dimensional first order quasilinear hyperbolic systems with general nonlinear boundary conditions. An implicit duality between the exact boundary controllability and the exact boundary observability is then shown in the quasilinear case. },
author = {Li, Tatsien},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Exact boundary observability; exact boundary controllability; semi-global C1 solution; mixed initial-boundary value problem; quasilinear hyperbolic system.; exact boundary observability; exact boundary controllability; semi-global solution; mixed initial-boundary value problem; quasilinear hyperbolic system},
language = {eng},
month = {1},
number = {4},
pages = {759-766},
publisher = {EDP Sciences},
title = {Exact boundary observability for quasilinear hyperbolic systems},
url = {http://eudml.org/doc/250273},
volume = {14},
year = {2008},
}

TY - JOUR
AU - Li, Tatsien
TI - Exact boundary observability for quasilinear hyperbolic systems
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2008/1//
PB - EDP Sciences
VL - 14
IS - 4
SP - 759
EP - 766
AB - By means of a direct and constructive method based on the theory of semi-global C1 solution, the local exact boundary observability is established for one-dimensional first order quasilinear hyperbolic systems with general nonlinear boundary conditions. An implicit duality between the exact boundary controllability and the exact boundary observability is then shown in the quasilinear case.
LA - eng
KW - Exact boundary observability; exact boundary controllability; semi-global C1 solution; mixed initial-boundary value problem; quasilinear hyperbolic system.; exact boundary observability; exact boundary controllability; semi-global solution; mixed initial-boundary value problem; quasilinear hyperbolic system
UR - http://eudml.org/doc/250273
ER -

References

top
  1. F. Alabau and V. Komornik, Observabilité, contrôlabilité et stabilisation frontière du système d'élasticité linéaire. C. R. Acad. Sci. Paris Sér. I Math.324 (1997) 519–524.  
  2. C. Bardos, G. Lebeau and R. Rauch, Sharp efficient conditions for the observation, control and stabilization of wave from the boundary. SIAM J. Control Optim. 30 (1992) 1024–1065.  Zbl0786.93009
  3. I. Lasiecka, R. Triggiani and P. Yao, Inverse/observability estimates for second-order hyperbolic equations with variable coefficients. J. Math. Anal. Appl. 235 (1999) 13–57.  Zbl0931.35022
  4. T. Li and Y. Jin, Semi-global C1 solution to the mixed initial-boundary value problem for quasilinear hyperbolic systems. Chin. Ann. Math. 22B (2001) 325–336.  Zbl1005.35058
  5. T. Li and B. Rao, Local exact boundary controllability for a class of quasilinear hyperbolic systems. Chin. Ann. Math.23B (2002) 209–218.  Zbl1184.35196
  6. T. Li and B. Rao, Exact boundary controllability for quasilinear hyperbolic systems. SIAM J. Control Optim.41 (2003) 1748–1755.  Zbl1032.35124
  7. J.-L. Lions, Contrôlabilité Exacte, Perturbations et Stabilisation de Systèmes Distribués, Tome I: Contrôlabilité Exacte, RMA 8. Masson (1988).  
  8. D.L. Russell, Controllability and stabilizability theory for linear partial differential equations: recent progress and open questions. SIAM Rev.20 (1978) 639–739.  Zbl0397.93001
  9. I. Trooshin and M. Yamamoto, Identification problem for a one-dimensional vibrating system. Math. Meth. Appl. Sci. 28 (2005) 2037–2059.  Zbl1083.35136
  10. Z. Wang, Exact controllability for nonautonomous first order quasilinear hyperbolic systems. Chin. Ann. Math. 27B (2006) 643–656.  Zbl1197.93062
  11. P. Yao, On the observability inequalities for exact controllability of wave equations with variable coefficients. SIAM J. Control Optim. 37 (1999) 1568–1599.  Zbl0951.35069
  12. E. Zuazua, Boundary observability for the space-discretization of the 1-D wave equation. C. R. Acad. Sci. Paris Sér. I Math.326 (1998) 713–718.  Zbl0910.65051
  13. E. Zuazua, Boundary observability for the finite-difference space semi-discretizations of the 2-D wave equation in the square. J. Math. Pures Appl. 78 (1999) 523–563.  Zbl0939.93016

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.