A unifying perspective on linear continuum equations prevalent in science. Part III: Canonical forms for dynamic equations with moduli that may, or may not, vary with time

TL;DR

This paper extends the extended abstract theory of composites to a wide range of dynamic equations, including those with time-varying moduli and moving media, unifying their canonical forms.

Contribution

It introduces a unifying framework for dynamic continuum equations with moduli that may vary in time, broadening the applicability of composite theory methods.

Findings

Unified canonical forms for dynamic equations

Extension of composite theory to time-varying media

Applicability to moving and changing media

Abstract

Enlarging on Parts I and II we write more equations in the desired format of the extended abstract theory of composites. We focus on a multitude of full dynamic equations, including equations where the medium is moving or otherwise changing in time. The motivation is that results and methods in the theory of composites then extend to these equations.