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

Abstract

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.