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arXiv · 1702.01988

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

Jan Burczak·Josef Málek·Piotr Minakowski
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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.

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Jan Burczak, Josef Málek, Piotr Minakowski. 2017-02-07. Stress-diffusive regularizations of non-dissipative rate-type materials. https://doi.org/10.3934/dcdss.2017067

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