# Stress-diffusive regularizations of non-dissipative rate-type materials

## TL;DR

This paper introduces stress-diffusive regularizations for non-dissipative elastic rate-type materials, enabling well-posedness of the model's equations where previous models lacked such guarantees.

## Contribution

The authors propose novel stress-diffusive regularizations that ensure well-posedness for elastic rate-type models, focusing on regularizations only in the stress evolution equation.

## Key findings

- Established well-posedness for regularized models in two-dimensional periodic settings.
- Demonstrated regularizations enable mathematical analysis of non-dissipative materials.
- Contrasted new results with existing models lacking such regularizations.

## Abstract

We consider non-dissipative (elastic) rate-type material models that are derived within the Gibbs-potential-based thermodynamic framework. Since the absence of any dissipative mechanism in the model prevents us from establishing even a local-in-time existence result in two spatial dimensions for a spatially periodic problem, we propose two regularisations. For such regularized problems we obtain well-posedness of the planar, spatially periodic problem. In contrast with existing results, we prove ours for a regularizing term present solely in the evolution equation for the stress.