Semi-global C1 solution and exact boundary controllability for reducible quasilinear hyperbolic systems

Ta-Tsien Li; Bopeng Rao; Yi Jin

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 2, page 399-408
  • ISSN: 0764-583X

Abstract

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By means of a result on the semi-global C1 solution, we establish the exact boundary controllability for the reducible quasilinear hyperbolic system if the C1 norm of initial data and final state is small enough.

How to cite

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Li, Ta-Tsien, Rao, Bopeng, and Jin, Yi. "Semi-global C1 solution and exact boundary controllability for reducible quasilinear hyperbolic systems." ESAIM: Mathematical Modelling and Numerical Analysis 34.2 (2010): 399-408. <http://eudml.org/doc/197397>.

@article{Li2010,
abstract = { By means of a result on the semi-global C1 solution, we establish the exact boundary controllability for the reducible quasilinear hyperbolic system if the C1 norm of initial data and final state is small enough. },
author = {Li, Ta-Tsien, Rao, Bopeng, Jin, Yi},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {reducible quasilinear hyperbolic system; semi-global C1 solution; exact boundary controllability.; hyperbolic systems; boundary control; exact controllability},
language = {eng},
month = {3},
number = {2},
pages = {399-408},
publisher = {EDP Sciences},
title = {Semi-global C1 solution and exact boundary controllability for reducible quasilinear hyperbolic systems},
url = {http://eudml.org/doc/197397},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Li, Ta-Tsien
AU - Rao, Bopeng
AU - Jin, Yi
TI - Semi-global C1 solution and exact boundary controllability for reducible quasilinear hyperbolic systems
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 2
SP - 399
EP - 408
AB - By means of a result on the semi-global C1 solution, we establish the exact boundary controllability for the reducible quasilinear hyperbolic system if the C1 norm of initial data and final state is small enough.
LA - eng
KW - reducible quasilinear hyperbolic system; semi-global C1 solution; exact boundary controllability.; hyperbolic systems; boundary control; exact controllability
UR - http://eudml.org/doc/197397
ER -

References

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  2. M. Cirinà, Nonlinear hyperbolic problems with solutions on preassigned sets. Michigan Math. J.17 (1970) 193-209.  Zbl0201.42702
  3. I. Lasiecka and R. Triggiani, Exact controllability of semilinear abstract systems with applications to waves and plates boundary control problems. Appl. Math. Optim.23 (1991) 109-154.  Zbl0729.93023
  4. Li Ta-tsien, Global Classical Solutions for Quasilinear Hyperbolic Systems. Research in Applied Mathematics32, Masson, John Wiley (1994).  Zbl0841.35064
  5. Li Ta-tsien and Zhang Bing-Yu, Global exact boundary controllability of a class of quasilinear hyperbolic systems. J. Math. Anal. Appl.225 (1998) 289-311.  Zbl0915.93007
  6. Li Ta-tsien and Yu Wen-ci, Boundary Value Problems for Quasilinear Hyperbolic Systems. Duck University, Mathematics Series V (1985).  
  7. J.-L. Lions, Contrôlabilité exacte, Perturbations et Stabilisation de Systèmes Distribués, Masson (1988) Vol. I.  Zbl0653.93002
  8. V. Komornik, Exact Controllability and Stabilization, The Multiplier Method, Masson, John Wiley (1994).  Zbl0937.93003
  9. 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
  10. E. Zuazua, Exact controllability for the semilinear wave equation. J. Math. Pures Appl.69 (1990) 1-32.  Zbl0638.49017

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