Gavioli, C., & Krejci, P. (2023). Degenerate diffusion with Preisach hysteresis. Discrete and Continuous Dynamical Systems - Series S, 16(12), 3677–3708. https://doi.org/10.3934/dcdss.2023154
Discrete and Continuous Dynamical Systems - Series S
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ISSN:
1937-1632
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Datum (veröffentlicht):
2023
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Umfang:
32
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Verlag:
AMER INST MATHEMATICAL SCIENCES-AIMS
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Peer Reviewed:
Ja
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Keywords:
Porous media; degenerate PDE; hysteresis; higher order energies; convexity
en
Abstract:
Fluid diffusion in unsaturated porous media manifests strong hysteresis effects due to surface tension on the liquid-gas interface. We describe hysteresis in the pressure-saturation relation by means of the Preisach operator, which makes the resulting evolutionary PDE strongly degenerate. We prove the existence and uniqueness of a strong global solution in arbitrary space dimension using a special weak convexity concept.
