The Biot-Allard poro-elasticity system: equivalent forms and well-posedness
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910469477892096 |
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| author | Stokke, Jakob S. Bause, Markus Margenberg, Nils Radu, Florin A. |
| author_facet | Stokke, Jakob S. Bause, Markus Margenberg, Nils Radu, Florin A. |
| contents | We consider the fully dynamic Biot-Allard model, which includes memory effects. Convolution integrals in time model the history of the porous medium. We use a series representation of the dynamic permeability in the frequency domain to rewrite the equations in a coupled system without convolution integrals, suitable for the design of efficient numerical approximation schemes. The main result is the well-posedness of the system, proved by the abstract theory of R. Picard for evolutionary problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01184 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Biot-Allard poro-elasticity system: equivalent forms and well-posedness Stokke, Jakob S. Bause, Markus Margenberg, Nils Radu, Florin A. Analysis of PDEs Numerical Analysis We consider the fully dynamic Biot-Allard model, which includes memory effects. Convolution integrals in time model the history of the porous medium. We use a series representation of the dynamic permeability in the frequency domain to rewrite the equations in a coupled system without convolution integrals, suitable for the design of efficient numerical approximation schemes. The main result is the well-posedness of the system, proved by the abstract theory of R. Picard for evolutionary problems. |
| title | The Biot-Allard poro-elasticity system: equivalent forms and well-posedness |
| topic | Analysis of PDEs Numerical Analysis |
| url | https://arxiv.org/abs/2406.01184 |