  This work considers a compressible, viscous, heat-conducting fluid exhibiting
thermal relaxation according to Christov's constitutive heat transfer law (C.
I. Christov, Mech. Research Comm. 36 (2009)), which is of Cattaneo type. The
resulting evolution equations are known as Cattaneo-Christov systems. In this
contribution, it is shown that Cattaneo-Christov systems for one-dimensional
compressible fluid flow are strictly dissipative. The proof is based on the
verification of a genuine coupling condition for hyperbolic-parabolic systems
with viscous and relaxation effects combined as well as on showing the
existence of compensating functions of the state variables in the sense of
Shizuta and Kawashima (Y. Shizuta and S. Kawashima, Hokkaido Math. J. 14
(1985)). This property is used to obtain linear decay rates for solutions to
the linearized equations around equilibrium states.
