  In this paper we deal with an abstract problem which includes the linearized
equations of coupled sound and heat flow as an example. Recently, a time
discretization of a simultaneous abstract evolution equation applying to some
parabolic-hyperbolic phase-field systems has been studied. This paper focuses
on a time discretization of an abstract problem applying to the linearized
equations of coupled sound and heat flow. Also, this paper gives some
parabolic-hyperbolic phase-field systems as examples.
