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March  2010, 28(1): 243-257. doi: 10.3934/dcds.2010.28.243

Exact boundary controllability and observability for first order quasilinear hyperbolic systems with a kind of nonlocal boundary conditions

Tatsien Li 1, , Bopeng Rao 2, and  Zhiqiang Wang 3,

1. 

School of Mathematical Sciences, Fudan University, 220 Handan Road, Shanghai 200433
2. 

Institut de Recherche Mathématique Avancée, Université de Strasbourg, 67084 Strasbourg, France
3. 

School of Mathematical Sciences, Fudan University, Shanghai 200433

Received  August 2009 Revised  November 2009 Published  April 2010

In this paper we establish the theory on the semiglobal classical solution to first order quasilinear hyperbolic systems with a kind of nonlocal boundary conditions, and based on this, the corresponding exact boundary controllability and observability are obtained by a constructive method. Moreover, with the linearized Saint-Venant system and the 1-D linear wave equation as examples, we show that the number of both boundary controls and boundary observations can not be reduced, and consequently, we conclude that the exact boundary controllability for a hyperbolic system in a network with loop can not be realized generically.
Keywords: exact boundary observability., Quasilinear hyperbolic system, nonlocal boundary conditions, exact boundary controllability.
Mathematics Subject Classification: Primary: 93B05, 93B07; Secondary: 35L5.
Citation: Tatsien Li, Bopeng Rao, Zhiqiang Wang. Exact boundary controllability and observability for first order quasilinear hyperbolic systems with a kind of nonlocal boundary conditions. Discrete and Continuous Dynamical Systems, 2010, 28 (1) : 243-257. doi: 10.3934/dcds.2010.28.243
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