Well posedness for a quasilinear generalisation of the matched microstructure model

TL;DR

This paper establishes the well-posedness of a quasilinear extension of the matched microstructure model using maximal regularity techniques in a Sobolev space framework.

Contribution

It introduces a novel quasilinear generalization of the matched microstructure model and proves its well-posedness with a maximal regularity approach.

Findings

Well-posedness proven in a strong Sobolev setting

Extension to quasilinear systems achieved

Maximal regularity method applied successfully

Abstract

We consider a generalisation to quasilinear systems of the matched microstructure model. The proof of well posedness in a strong Sobolev setting is based on an approach via maximal regularity.