Deformable porous media with degenerate hysteresis in gravity field
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 convexifi...
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| Language: | English |
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AIMS Press
2025-02-01
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| Series: | Mathematics in Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.2025003 |
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| author | Chiara Gavioli Pavel Krejčí |
| author_facet | Chiara Gavioli Pavel Krejčí |
| author_sort | Chiara Gavioli |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3926cc5337ee421097aab09d56dac79f |
| institution | OA Journals |
| issn | 2640-3501 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj-art-3926cc5337ee421097aab09d56dac79f2025-08-20T01:57:05ZengAIMS PressMathematics in Engineering2640-35012025-02-0171356010.3934/mine.2025003Deformable porous media with degenerate hysteresis in gravity fieldChiara Gavioli0Pavel Krejčí1Faculty of Civil Engineering, Czech Technical University, Thákurova 7, CZ-16629 Praha 6, Czech RepublicFaculty of Civil Engineering, Czech Technical University, Thákurova 7, CZ-16629 Praha 6, Czech RepublicHysteresis 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.https://www.aimspress.com/article/doi/10.3934/mine.2025003hysteresisdegenerate equationporous mediaviscoelasticitygravity effects |
| spellingShingle | Chiara Gavioli Pavel Krejčí Deformable porous media with degenerate hysteresis in gravity field Mathematics in Engineering hysteresis degenerate equation porous media viscoelasticity gravity effects |
| title | Deformable porous media with degenerate hysteresis in gravity field |
| title_full | Deformable porous media with degenerate hysteresis in gravity field |
| title_fullStr | Deformable porous media with degenerate hysteresis in gravity field |
| title_full_unstemmed | Deformable porous media with degenerate hysteresis in gravity field |
| title_short | Deformable porous media with degenerate hysteresis in gravity field |
| title_sort | deformable porous media with degenerate hysteresis in gravity field |
| topic | hysteresis degenerate equation porous media viscoelasticity gravity effects |
| url | https://www.aimspress.com/article/doi/10.3934/mine.2025003 |
| work_keys_str_mv | AT chiaragavioli deformableporousmediawithdegeneratehysteresisingravityfield AT pavelkrejci deformableporousmediawithdegeneratehysteresisingravityfield |