Global existence and uniqueness of weak solutions for a Willis-type model of elastodynamics
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917105827315712 |
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| author | Blesgen, Thomas Neff, Patrizio |
| author_facet | Blesgen, Thomas Neff, Patrizio |
| contents | The existence and uniqueness of weak solutions is shown for a system related to the Willis model of elastodynamics. Both the whole space case and the case of a bounded smooth domain are studied. To this end the equations are reformulated as a linear symmetric hyperbolic system of first order and the existing theory for such systems is applied. If the initial and boundary data is regular enough, classical solutions are obtained. The possibility to transform the problem to a linear symmetric hyperbolic system hinges on a new symmetry condition on the Willis coupling tensor S, not yet considered in the literature. This condition demands that S is a totally symmetric third-order tensor. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_05437 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global existence and uniqueness of weak solutions for a Willis-type model of elastodynamics Blesgen, Thomas Neff, Patrizio Analysis of PDEs 35A01, 35L50, 35Q74, 74B20 The existence and uniqueness of weak solutions is shown for a system related to the Willis model of elastodynamics. Both the whole space case and the case of a bounded smooth domain are studied. To this end the equations are reformulated as a linear symmetric hyperbolic system of first order and the existing theory for such systems is applied. If the initial and boundary data is regular enough, classical solutions are obtained. The possibility to transform the problem to a linear symmetric hyperbolic system hinges on a new symmetry condition on the Willis coupling tensor S, not yet considered in the literature. This condition demands that S is a totally symmetric third-order tensor. |
| title | Global existence and uniqueness of weak solutions for a Willis-type model of elastodynamics |
| topic | Analysis of PDEs 35A01, 35L50, 35Q74, 74B20 |
| url | https://arxiv.org/abs/2504.05437 |