A unifying perspective on linear continuum equations prevalent in science. Part I: Canonical forms for static, steady, and quasistatic equations

TL;DR

This paper reformulates a broad class of linear continuum equations using composite theory, providing a unifying framework for understanding and solving static, steady, and quasistatic equations in science.

Contribution

It introduces a unifying reformulation of linear continuum equations through the extended abstract theory of composites, enhancing understanding and solution strategies.

Findings

Unified form for static, steady, and quasistatic equations

Application of composite theory to linear continuum equations

Facilitates more efficient solution methods

Abstract

Following some past advances, we reformulate a large class of linear continuum science equations in the format of the extended abstract theory of composites so that we can apply this theory to better understand and efficiently solve those equations. Here in part I we elucidate the form for many static, steady, and quasistatic equations.