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2010, Volume 28, Issue 1: 243-257. Doi: 10.3934/dcds.2010.28.243
This issue Previous Article Two-point closure based large-eddy simulations in turbulence. Part 2: Inhomogeneous cases Next Article Models & measures of mixing & effective diffusion

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

  • 1.

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

  • 2.

    Institut de Recherche Mathématique Avancée, Université de Strasbourg, 67084 Strasbourg

  • 3.

    School of Mathematical Sciences, Fudan University, Shanghai 200433

Received:  July 31, 2009
Revised:  October 31, 2009
Published:  February 2010
Abstract Related Papers Cited by
    Abstract
  • 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.
    Mathematics Subject Classification: Primary: 93B05, 93B07; Secondary: 35L50.

    Citation:
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