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January  2009, 8(1): 405-418. doi: 10.3934/cpaa.2009.8.405

A note on the one-side exact boundary controllability for quasilinear hyperbolic systems

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

1. 

School of Mathematical Sciences, Fudan University, Shanghai 200433
2. 

Institut de Recherche Mathématique Avancée, Université Louis Pasteur de Strasbourg, 7 rue René-Descartes, 67084 Strasbourg

Received  March 2008 Revised  August 2008 Published  October 2008

The known theory on the one-side exact boundary controllability for first order quasilinear hyperbolic systems requires that the unknown variables are suitably coupled or satisfy the Group Property in boundary conditions at the non-control side (see [5],[10]). In this paper we illustrate, with an inspiring example, that the one-side exact boundary controllability can still be realized by means of a suitable coupling among the unknown variables in the quasilinear hyperbolic system itself instead of in boundary conditions.
Keywords: First order quasilinear hyperbolic system, second order quasilinear hyperbolic equation, semi-global classical solution, one-side exact boundary controllability.
Mathematics Subject Classification: Primary: 35L50, 93C20; Secondary: 93B05.
Citation: Tatsien Li, Bopeng Rao, Zhiqiang Wang. A note on the one-side exact boundary controllability for quasilinear hyperbolic systems. Communications on Pure & Applied Analysis, 2009, 8 (1) : 405-418. doi: 10.3934/cpaa.2009.8.405
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