Existence and weak-strong uniqueness for damage systems in viscoelasticity
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916377172901888 |
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| author | Lasarzik, Robert Rocca, Elisabetta Rossi, Riccarda |
| author_facet | Lasarzik, Robert Rocca, Elisabetta Rossi, Riccarda |
| contents | In this paper we investigate the existence of solutions and their weak-strong uniqueness property for a PDE system modelling damage in viscoelastic materials. In fact, we address two solution concepts, weak and strong solutions. For the former, we obtain a global-in-time existence result, but the highly nonlinear character of the system prevents us from proving their uniqueness. For the latter, we prove local-in-time existence. Then, we show that the strong solution, as long as it exists, is unique in the class of weak solutions. This weak-strong uniqueness statement is proved by means of a suitable relative energy inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00528 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence and weak-strong uniqueness for damage systems in viscoelasticity Lasarzik, Robert Rocca, Elisabetta Rossi, Riccarda Analysis of PDEs In this paper we investigate the existence of solutions and their weak-strong uniqueness property for a PDE system modelling damage in viscoelastic materials. In fact, we address two solution concepts, weak and strong solutions. For the former, we obtain a global-in-time existence result, but the highly nonlinear character of the system prevents us from proving their uniqueness. For the latter, we prove local-in-time existence. Then, we show that the strong solution, as long as it exists, is unique in the class of weak solutions. This weak-strong uniqueness statement is proved by means of a suitable relative energy inequality. |
| title | Existence and weak-strong uniqueness for damage systems in viscoelasticity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.00528 |