A unifying perspective on linear continuum equations prevalent in science. Part IV: Canonical forms for equations involving higher order gradients

TL;DR

This paper extends the extended abstract theory of composites to a wide range of higher order gradient equations, providing a unifying framework that broadens the applicability of composite material analysis methods.

Contribution

It introduces canonical forms for higher order gradient equations, enabling the extension of composite theory results to these complex equations.

Findings

Unified framework for higher order gradient equations

Extension of composite theory to new classes of equations

Facilitates analysis of complex systems with higher derivatives

Abstract

Enlarging on Parts I, II, and III we write more equations in the desired format of the extended abstract theory of composites. We focus on a multitude of equations involving higher order derivatives. The motivation is that results and methods in the theory of composites then extend to these equations.