Degenerate diffusion with Preisach hysteresis
arXiv:2303.17451 · doi:10.3934/dcdss.2023154
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.
arXiv comment34 pages
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