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Semi-global C 1 solution and exact boundary controllabilityfor reducible quasilinear hyperbolic systems

Published online by Cambridge University Press:  15 April 2002

Ta-Tsien Li ,
Bopeng Rao  and
Yi Jin
Ta-Tsien Li
Affiliation:
Department of Mathematics, Fudan University, Shanghai 20043, P.R. China.
Bopeng Rao
Affiliation:
Institut de Recherche Mathématique Avancée, Université Louis Pasteur de Strasbourg, 7 rue René-Descartes, 67084 Strasbourg, France.
Yi Jin
Affiliation:
Institut de Recherche Mathématique Avancée, Université Louis Pasteur de Strasbourg, 7 rue René-Descartes, 67084 Strasbourg, France.
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Abstract

By means of a result on the semi-global C 1 solution, we establish the exact boundary controllability for the reducible quasilinearhyperbolic system if the C 1 norm of initial data and final state issmall enough.

Keywords

reducible quasilinear hyperbolic systemsemi-global C 1 solutionexact boundary controllability.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 2: Special issue for R. Teman's 60th birthday , March 2000 , pp. 399 - 408
Copyright
© EDP Sciences, SMAI, 2000

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References

Cirià, M., Boundary controllability of nonlinear hyperbolic systems. SIAM J. Control 7 (1969) 198-212. CrossRef
Cirinà, M., Nonlinear hyperbolic problems with solutions on preassigned sets. Michigan Math. J. 17 (1970) 193-209.
Lasiecka, I. and Triggiani, R., Exact controllability of semilinear abstract systems with applications to waves and plates boundary control problems. Appl. Math. Optim. 23 (1991) 109-154. CrossRef
Li Ta-tsien, Global Classical Solutions for Quasilinear Hyperbolic Systems. Research in Applied Mathematics 32, Masson, John Wiley (1994).
Ta-tsien, Li and Bing-Yu, Zhang, Global exact boundary controllability of a class of quasilinear hyperbolic systems. J. Math. Anal. Appl. 225 (1998) 289-311.
Li Ta-tsien and Yu Wen-ci, Boundary Value Problems for Quasilinear Hyperbolic Systems. Duck University, Mathematics Series V (1985).
J.-L. Lions, Contrôlabilité exacte, Perturbations et Stabilisation de Systèmes Distribués, Masson (1988) Vol. I.
V. Komornik, Exact Controllability and Stabilization, The Multiplier Method, Masson, John Wiley (1994).
Russell, D.L., Controllability and stabilizability theory for linear partial differential equations. Recent progress and open questions. SIAM Rev. 20 (1978) 639-739. CrossRef
Zuazua, E., Exact controllability for the semilinear wave equation. J. Math. Pures Appl. 69 (1990) 1-32.