Stress-diffusive regularizations of non-dissipative rate-type materials
Analysis of PDEs
2017-07-20 v1
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.
Cite
@article{arxiv.1702.01988,
title = {Stress-diffusive regularizations of non-dissipative rate-type materials},
author = {Jan Burczak and Josef Málek and Piotr Minakowski},
journal= {arXiv preprint arXiv:1702.01988},
year = {2017}
}