[hal-01064805] Tikhonov theorem for linear hyperbolic systems

Systems modelled by linear singularly perturbed partial differential equations are considered in this paper Precisely a 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



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