Exact controllability for first order quasilinear hyperbolic systems with internal controls

Internal Controllability of First Order Quasi-linear Hyperbolic Systems with a Reduced Number of Controls

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...

Exact 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...

Hyperbolic to Parabolic Relaxation Theory for Quasilinear First Order Systems

In this paper we study the limiting behavior of nonhomogeneous hyperbolic systems of balance laws when the relaxed equilibria are described by means of systems of parabolic type. In particular we obtain a complete theory for the 22 systems of genuinely nonlinear hyperbolic balance laws in 1-D with a strong dissipative term. A diierent method, which combines the div-curl lemma with accretive ope...

Semi-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.