A local and global well-posedness results for the general stress-assisted diffusion systems

TL;DR

This paper establishes local and global existence results for classical solutions to broad classes of stress-assisted diffusion systems, relevant in non-Euclidean elasticity and liquid crystal elastomers.

Contribution

It provides the first comprehensive well-posedness results for these general stress-assisted diffusion models, extending previous work in the field.

Findings

Proved local existence of solutions.

Established global existence under certain conditions.

Applicable to non-Euclidean elasticity and liquid crystal elastomers.

Abstract

We prove the local and global in time existence of the classical solutions to two general classes of the stress-assisted diffusion systems. Our results are applicable in the context of the non-Euclidean elasticity and liquid crystal elastomers.