G-convergence of Friedrichs systems revisited

TL;DR

This paper revisits homogenisation theory for Friedrichs systems, demonstrating that $G$-compactness can be achieved under weaker assumptions, thus broadening its applicability to systems with memory effects without relying on traditional compactness techniques.

Contribution

It extends $G$-compactness results for Friedrichs systems to weaker assumptions, enabling analysis of systems with memory effects and avoiding traditional compactness methods.

Findings

$G$-compactness achieved under weaker assumptions

Applicability to systems with memory effects

Avoids traditional compactness techniques

Abstract

We revisit homogenisation theory for Friedrichs systems. In particular, we show that $G$-compactness can be obtained under severely weaker assumptions than in the original work of Burazin and Vrdoljak (2014). In this way we extend the applicability of $G$-compactness results for Friedrichs systems to equations that yield memory effects in the homogenised limit and detour any usage of compactness techniques previously employed.