English

The Biot-Allard poro-elasticity system: equivalent forms and well-posedness

Analysis of PDEs 2024-06-04 v1 Numerical Analysis Numerical Analysis

Abstract

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.

Keywords

Cite

@article{arxiv.2406.01184,
  title  = {The Biot-Allard poro-elasticity system: equivalent forms and well-posedness},
  author = {Jakob S. Stokke and Markus Bause and Nils Margenberg and Florin A. Radu},
  journal= {arXiv preprint arXiv:2406.01184},
  year   = {2024}
}