Local well-posedness for Fr\'emond's model of complete damage in elastic solids

TL;DR

This paper proves the local well-posedness of Frémond's damage model in elastic solids without relying on regularizing terms, establishing existence and uniqueness of solutions.

Contribution

It demonstrates local well-posedness for Frémond's damage model without regularization, a significant advancement over prior work.

Findings

Existence of local strong solutions

Uniqueness of solutions

No regularizing terms needed

Abstract

We consider a model for the evolution of damage in elastic materials originally proposed by Michel Fr\'emond. For the corresponding PDE system we prove existence and uniqueness of a local in time strong solution. The main novelty of our result stands in the fact that, differently from previous contributions, we assume no occurrence of any type of regularizing terms.