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arXiv · 2303.17451

Degenerate diffusion with Preisach hysteresis

Chiara Gavioli·Pavel Krejčí
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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.

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Chiara Gavioli, Pavel Krejčí. 2023-03-30. Degenerate diffusion with Preisach hysteresis. https://doi.org/10.3934/dcdss.2023154

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