Time discretization of an abstract problem applying to the linearized equations of coupled sound and heat flow

Abstract: 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.