Degenerate diffusion with Preisach hysteresis
Analysis of PDEs
2023-12-19 v2
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.
Cite
@article{arxiv.2303.17451,
title = {Degenerate diffusion with Preisach hysteresis},
author = {Chiara Gavioli and Pavel Krejčí},
journal= {arXiv preprint arXiv:2303.17451},
year = {2023}
}
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34 pages