We study the effects of a composition gradient and of a non vanishing heat
flux on the phase velocity of thermal waves along a graded system. We take into account non-local and non-linear effects
by applying a generalized heat transport equation. We compare the results for high-frequency
and low-frequency waves. For low frequency, we discuss the conditions in which thermal waves may
propagate in SixGe1-x and (Bi1-xSbx)2Te3 systems. For high frequency, we discuss the influence
of the relaxation of the flux of the heat flux on the heat wave propagation
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