Biot’s poro-elasticity system with dynamic permeability convolution: well-posedness for evolutionary form

Stokke, Jakob S.; Bause, Markus; Margenberg, Nils; Radu, Florin A.

doi:10.1016/j.aml.2024.109224

Biot’s poro-elasticity system with dynamic permeability convolution: well-posedness for evolutionary form

Publication date

2024-07-14

Document type

Forschungsartikel

Author

Stokke, Jakob S.

Bause, Markus

Margenberg, Nils

Radu, Florin A.

Organisational unit

Numerische Mathematik

DOI

10.1016/j.aml.2024.109224

URI

https://openhsu.ub.hsu-hh.de/handle/10.24405/20902

Publisher

Elsevier

Series or journal

Applied Mathematics Letters

ISSN

0893-9659

Periodical volume

158

Article ID

109224

Peer-reviewed

✅

Part of the university bibliography

✅

Language

English

Abstract

We consider Biot’s equations of poroelasticity where the development of viscous boundary layers in the pores is allowed for by using a dynamic permeability convolution operator in the time domain. This system with memory effects is also referred to as the dynamic Biot–Allard model. We use a series representation of the dynamic permeability in the frequency domain to rewrite the equations in the time domain in a coupled system without convolution integrals, which is also suitable for designing efficient numerical approximation schemes. The main result here is the well-posedness of the system, rewritten in evolutionary form, which is proved by an abstract theory for evolutionary problems.

Description

This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Version

Published version

Access right on openHSU

Metadata only access