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

Tatsien Li; Bopeng Rao; Zhiqiang Wang

doi:10.3934/cpaa.2009.8.405

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2009, Volume 8, Issue 1: 405-418. Doi: 10.3934/cpaa.2009.8.405

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

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: February 29, 2008

Revised: July 31, 2008

Published: December 2008

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Abstract

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.

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Mathematics Subject Classification: Primary: 35L50, 93C20; Secondary: 93B05.

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