✦ LIBER ✦

Diffusion in poro-plastic media

✍ Scribed by R. E. Showalter; U. Stefanelli

Publisher: John Wiley and Sons
Year: 2004
Tongue: English
Weight: 188 KB
Volume: 27
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.541

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✦ Synopsis

Abstract

A model is developed for the flow of a slightly compressible fluid through a saturated inelastic porous medium. The initial‐boundary‐value problem is a system that consists of the diffusion equation for the fluid coupled to the momentum equation for the porous solid together with a constitutive law which includes a possibly hysteretic relation of elasto‐visco‐plastic type. The variational form of this problem in Hilbert space is a non‐linear evolution equation for which the existence and uniqueness of a global strong solution is proved by means of monotonicity methods. Various degenerate situations are permitted, such as incompressible fluid, negligible porosity, or a quasi‐static momentum equation. The essential sufficient conditions for the well‐posedness of the system consist of an ellipticity condition on the term for diffusion of fluid and either a viscous or a hardening assumption in the constitutive relation for the porous solid. Copyright © 2004 John Wiley & Sons, Ltd.

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