DISPERSION-RELATION IN THE HIGH-FREQUENCY LIMIT AND NONLINEAR-WAVE STABILITY FOR HYPERBOLIC DISSIPATIVE SYSTEMS

We consider a quasi-linear first order hyperbolic dissipative system in a one-dimensional space, and we prove that, if the constant solutions are stable for the linearized system, then they are also non-linear asymptotically lambda-stable, i.e. the amplitude of the discontinuity wave vanishes, when t increases, provided that the initial amplitude is sufficiently small. In order to give the proof an evaluation of the dispersion law in the limit of high frequencies is accomplished, and the results are applied to the case of the Extended Thermodynamics for a non-equilibrium monatomic classical gas.