Dispersion relation in the high frequency limit and non linear wave stability for hyperbolic dissipative systems

Wave features for consistent-order-extended thermodynamics

“…The frequency dependence of the phase velocity and of the attenuation is illustrated in Figure 2, where we also compare our results (solid lines) with the ones of Extended Thermodynamics at thirteen moments (dashed lines) [3] and with the experimental data (dots) [5]. It is easy to see that our results agree fairly well with the experimental data for low frequency, whereas there are some discrepancies for high frequency.…”

“…In passing we point out that the coefficient b is related to the high frequency limit of the attenuation of plane harmonic wave by [3] …”

“…whose value is greater than the corresponding one of Extended Thermodynamics at thirteen moments [3]. We note that b is a positive quantity and therefore Consistent-Order-Extended Thermodynamics of the third order satisfies the linear and the nonlinear stability with respect to this wave [11].…”

“…Frequency dependence of the phase velocity and of the attenuation is shown and our results are compared with those obtained in the context of Extended Thermodynamics at thirteen moments [3] and with the experimental data [5].…”

“…In this framework, sound waves in a gas have already been studied [3], while the propagation of sound waves in Extended Thermodynamics with many moments has been analyzed in [4], where the author proved that the higher is the number of the moments taken into account, 848 E. Barbera and G. Valenti ZAMP the better is the agreement of the phase velocity of the sound wave with the experimental data. In particular, for low frequencies few moments are sufficient, while for high frequencies the number of the moments must be increased.…”