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

TL;DR

This paper develops a time discretization method for an abstract problem that encompasses the linearized equations of coupled sound and heat flow, with applications to phase-field systems.

Contribution

It introduces a novel time discretization approach for the coupled sound and heat flow equations within an abstract framework, extending previous methods to new systems.

Findings

Effective discretization of coupled sound and heat equations

Application to phase-field systems demonstrated

Framework generalizes to other parabolic-hyperbolic systems

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.