EXPONENTIAL DECAY-RATES IN QUASI-LINEAR HYPERBOLIC HEAT-CONDUCTION

We study different exponential decay rates that appear in quasi-linear symmetric hyperbolic systems describing heat conduction models in the context of extended thermodynamics. In normal conditions they are des cribed using two different time scales. We show, after a study of the Cauchy problem for these systems, that for initial data close enough t o equilibrium, the solutions exist globally in time and decay exponent ially with the shortest relaxation time to the classical (Fourier's th eory) solutions; then they continue decaying exponentially to equilibr ium with the larger decaying time.