Long-time behaviour of a porous medium model with degenerate hysteresis

Author:

Gavioli Chiara1ORCID,Krejčí Pavel2ORCID

Affiliation:

1. Institute of Analysis and Scientific Computing, TU Wien, Wiedner Hauptstraße 8-10, Vienna A-1040, Austria

2. Faculty of Civil Engineering, Czech Technical University, Thákurova 7, Praha 6 CZ-16629, Czech Republic

Abstract

Hysteresis in the pressure-saturation relation in unsaturated porous media, owing to surface tension on the liquid–gas interface, exhibits strong degeneracy in the resulting mass balance equation. As an extension of previous existence and uniqueness results, we prove that under physically admissible initial conditions and without mass exchange with the exterior, the unique global solution of the fluid diffusion problem exists and asymptotically converges as time tends to infinity to a possibly non-homogeneous mass distribution and an a priori unknown constant pressure. This article is part of the theme issue ‘Non-smooth variational problems with applications in mechanics’.

Funder

OeAD-GmbH

Austrian Science Fund

Publisher

The Royal Society

Reference12 articles.

1. Differential Models of Hysteresis

2. Degenerate diffusion with Preisach hysteresis

3. �ber die magnetische Nachwirkung

4. Krejčí P. 1996 Hysteresis, convexity and dissipation in hyperbolic equations. In GAKUTO International series. mathematical sciences and applications, vol. 8. Tokyo: Gakkotosho.

5. A Generalized Prandtl–Ishlinskii Model for Hysteresis Modeling in Electromagnetic Devices

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1. Non-smooth variational problems and applications in mechanics;Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences;2024-07-15

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