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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.04152 |
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| _version_ | 1866915612586934272 |
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| author | Cieślak, Tomasz Owczarek, Sebastian Wielgos, Karolina |
| author_facet | Cieślak, Tomasz Owczarek, Sebastian Wielgos, Karolina |
| contents | In this article, we study a thermodynamically consistent thermo-visco-elastic model describing the balance of internal energy in a heat-conducting inelastic body. In the considered problem, the temperature dependence appears in both the elastic and inelastic constitutive relations. For such a system, we introduce the concept of a weak entropy-energy solution, which satisfies the entropy equality instead of the internal energy equation. Although the model does not possess any mathematically favorable structural properties, such as Kelvin-Voigt type effects or simplifications eliminating temperature from the constitutive relations, we prove the global-in-time existence of weak entropy-energy solutions for large initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04152 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entropy-energy solutions for Thermo-Visco-Elastic systems with Mróz-type inelastic behavior Cieślak, Tomasz Owczarek, Sebastian Wielgos, Karolina Analysis of PDEs In this article, we study a thermodynamically consistent thermo-visco-elastic model describing the balance of internal energy in a heat-conducting inelastic body. In the considered problem, the temperature dependence appears in both the elastic and inelastic constitutive relations. For such a system, we introduce the concept of a weak entropy-energy solution, which satisfies the entropy equality instead of the internal energy equation. Although the model does not possess any mathematically favorable structural properties, such as Kelvin-Voigt type effects or simplifications eliminating temperature from the constitutive relations, we prove the global-in-time existence of weak entropy-energy solutions for large initial data. |
| title | Entropy-energy solutions for Thermo-Visco-Elastic systems with Mróz-type inelastic behavior |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.04152 |