Tikhonov theorem for linear hyperbolic systems

International audienceA class of linear systems of conservation laws with a small perturbation parameter is introduced. By setting the perturbation parameter to zero, two subsystems, the reduced system standing for the slow dynamics and the boundary-layer system representing the fast dynamics, are computed. It is first proved that the exponential stability of the full system implies the stability of both subsystems. Secondly, a counter example is given to indicate that the converse is not true. Moreover a new Tikhonov theorem for this class of the infinite dimensional systems is stated. The solution of the full system can be approximated by that of the reduced system, and this is proved by Lyapunov techniques. An application to boundary feedback stabilization of gas transport model is used to illustrate the results