Stress-diffusive regularizations of non-dissipative rate-type materials
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 s...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2017
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| In: |
Discrete and continuous dynamical systems
Year: 2017, Volume: 10, Issue: 6, Pages: 1233-1256 |
| ISSN: | 1937-1179 |
| DOI: | 10.3934/dcdss.2017067 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.3934/dcdss.2017067 Verlag, Volltext: http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=14258 
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| Author Notes: | Jan Burczak, Josef Málek, Piotr Minakowski |
| Summary: | 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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| Item Description: | Revised February 2017 Gesehen am 08.06.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1937-1179 |
| DOI: | 10.3934/dcdss.2017067 |