The Biot-Allard poro-elasticity system: equivalent forms and well-posedness
<|reference_start|>The Biot-Allard poro-elasticity system: equivalent forms and well-posedness: 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.<|reference_end|>
@article{stokke2024the,
    title={The Biot-Allard poro-elasticity system: equivalent forms and
  well-posedness},
    author={Jakob S. Stokke, Markus Bause, Nils Margenberg, Florin A. Radu},
    journal={arXiv preprint arXiv:2406.01184},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.01184},
    primaryClass={math.AP cs.NA math.NA}
}