Record link: 
http://hdl.handle.net/20.500.12708/190428
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Title: 
Degenerate diffusion with Preisach hysteresis
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Citation: 
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
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Publisher DOI: 
10.3934/dcdss.2023154
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Publication Type: 
Article - Original Research Article
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Language: 
English
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Authors: 
Gavioli, Chiara 
Krejci, Pavel 
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Organisational Unit: 
E101-01-3 - Forschungsgruppe Mehrskalen Variationsrechnung 
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Journal: 
Discrete and Continuous Dynamical Systems - Series S 
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ISSN: 
1937-1632
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Date (published): 
2023
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Number of Pages: 
32
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Publisher: 
AMER INST MATHEMATICAL SCIENCES-AIMS
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Peer reviewed: 
Yes
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Keywords: 
Porous media; degenerate PDE; hysteresis; higher order energies; convexity
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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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Research Areas: 
Fundamental Mathematics Research: 100%
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Science Branch: 
1010 - Mathematik: 100%
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