Deformable porous media with degenerate hysteresis in gravity field

Chiara Gavioli; Pavel Krejčí; Chiara Gavioli; Pavel Krejčí

doi:10.3934/mine.2025003

Mathematics in Engineering

2025, Volume 7, Issue 1: 35-60. doi: 10.3934/mine.2025003

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Deformable porous media with degenerate hysteresis in gravity field

Chiara Gavioli ^{1
,
,},
Pavel Krejčí ^1,2

1.
Faculty of Civil Engineering, Czech Technical University, Thákurova 7, CZ-16629 Praha 6, Czech Republic
2.
Institute of Mathematics, Czech Academy of Sciences, Žitná 25, CZ-11567 Praha 1, Czech Republic

Received: 20 May 2024 Revised: 21 January 2025 Accepted: 09 February 2025 Published: 17 February 2025

Hysteresis in the pressure-saturation relation in unsaturated porous media, which is due to surface tension on the liquid-gas interface, exhibits strong degeneracy in the resulting mass balance equation. Solutions to such degenerate equations have been recently constructed by the method of convexification even if the permeability coefficient depends on the hysteretic saturation. The model is extended here to the case that the solid matrix material is viscoelastic and that the system is coupled with a gravity-driven moisture flux. The existence of a solution is proved by compact anisotropic embedding involving Orlicz spaces with respect to the time variable.
- hysteresis,
- degenerate equation,
- porous media,
- viscoelasticity,
- gravity effects
Citation: Chiara Gavioli, Pavel Krejčí. Deformable porous media with degenerate hysteresis in gravity field[J]. Mathematics in Engineering, 2025, 7(1): 35-60. doi: 10.3934/mine.2025003

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Abstract

Hysteresis in the pressure-saturation relation in unsaturated porous media, which is due to surface tension on the liquid-gas interface, exhibits strong degeneracy in the resulting mass balance equation. Solutions to such degenerate equations have been recently constructed by the method of convexification even if the permeability coefficient depends on the hysteretic saturation. The model is extended here to the case that the solid matrix material is viscoelastic and that the system is coupled with a gravity-driven moisture flux. The existence of a solution is proved by compact anisotropic embedding involving Orlicz spaces with respect to the time variable.

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