EXACT BOUNDARY OBSERVABILITY FOR QUASILINEAR HYPERBOLIC SYSTEMS 761 Remark 1
نویسندگان
چکیده
By means of a direct and constructive method based on the theory of semi-global C solution, the local exact boundary observability is established for one-dimensional first order quasilinear hyperbolic systems with general nonlinear boundary conditions. An implicit duality between the exact boundary controllability and the exact boundary observability is then shown in the quasilinear case. Mathematics Subject Classification. 35B37, 93C20, 35L50, 93B07, 35R30 Received February 13, 2006. Revised April 2, 2007. Published online January 30, 2008.
منابع مشابه
Exact boundary controllability and observability for first order quasilinear hyperbolic systems with a kind of nonlocal boundary conditions
In this paper we establish the theory on 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 1D linear wave equation as examples, we show that th...
متن کاملExact boundary observability for nonautonomous quasilinear wave equations
By means of a direct and constructive method based on the theory of semiglobal C solution, the local exact boundary observability is shown for nonautonomous 1-D quasilinear wave equations. The essential difference between nonautonomous wave equations and autonomous ones is also revealed.
متن کاملExact Boundary Controllability for 1-D Quasilinear Hyperbolic Systems with a Vanishing Characteristic Speed
The general theory on exact boundary controllability for general first order quasilinear hyperbolic systems requires that the characteristic speeds of the system do not vanish. This paper deals with exact boundary controllability, when this is not the case. Some important models are also shown as applications of the main result. The strategy uses the return method, which allows one in certain s...
متن کاملSemi-global C1 solution and exact boundary controllability for reducible quasilinear hyperbolic systems
By means of a result on the semi-global C solution, we establish the exact boundary controllability for the reducible quasilinear hyperbolic system if the C norm of initial data and final state is small enough. Mathematics Subject Classification. 35L50, 49J20, 49N50. Received: October 28, 1999. Revised: November 22, 1999.
متن کاملGlobal Classical Solutions to a Kind of Mixed Initial-Boundary Value Problem for Inhomogeneous Quasilinear Hyperbolic Systems
Abstract In this paper, the mixed initial-boundary value problem for inhomogeneous quasilinear strictly hyperbolic systems with nonlinear boundary conditions in the first quadrant {(t, x)| t ≥ 0, x ≥ 0} is investigated. Under the assumption that the right hand side satisfies matching condition and the system is strictly hyperbolic and weakly linearly degenerate, we obtain the global existence a...
متن کامل