Global exact boundary observability for first-order quasilinear hyperbolic systems of diagonal form

2012 ◽  
Vol 35 (13) ◽  
pp. 1505-1517 ◽  
Author(s):  
Lixin Yu
Keyword(s):  
Hyperbolic Systems ◽  
Diagonal Form ◽  
Quasilinear Hyperbolic Systems ◽  
First Order ◽  
Exact Boundary ◽  
Boundary Observability ◽  
Exact Boundary Observability

A Note on the One-Side Exact Boundary Observability for Quasilinear Hyperbolic Systems

2008 ◽  
Vol 15 (3) ◽  
pp. 571-580
Author(s):  
Tatsien Li ◽  
Bopeng Rao ◽  
Zhiqiang Wang
Keyword(s):  
Boundary Conditions ◽  
Hyperbolic Systems ◽  
Exact Boundary Controllability ◽  
Boundary Controllability ◽  
Quasilinear Hyperbolic Systems ◽  
First Order ◽  
Exact Boundary ◽  
The One ◽  
Boundary Observability ◽  
Exact Boundary Observability

Abstract The known theory on the one-side exact boundary observability for first order quasilinear hyperbolic systems requires that the unknown variables are suitably coupled or satisfy the Group Property in boundary conditions on the non-observation side (see [Tatsien, C. R. Math. Acad. Sci. 342: 937–942, 2006]–[Tatsien, ESAIM Control Optim. Calc. Var.], [Russell, SIAM Rev. 20: 639–739, 1978]). In this paper we illustrate, with an inspiring example, that the one-side exact boundary observability can be realized by means of a suitable coupling of the unknown variables in quasilinear hyperbolic system itself instead of in boundary conditions. Moreover, an implicit duality between the one-side exact boundary controllability and one-side exact boundary observability is also revealed in this situation.

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