Degenerate diffusion with Preisach hysteresis
Copyright policy )Degenerate diffusion with Preisach hysteresis
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.
34 pages
Equations with nonlinear hysteresis operators, porous media, higher-order energies, Mathematics - Analysis of PDEs, hysteresis, convexity, 35K65, 47J40, 74N30, FOS: Mathematics, Problems involving hysteresis in solids, Degenerate parabolic equations, degenerate PDE, Analysis of PDEs (math.AP)
Equations with nonlinear hysteresis operators, porous media, higher-order energies, Mathematics - Analysis of PDEs, hysteresis, convexity, 35K65, 47J40, 74N30, FOS: Mathematics, Problems involving hysteresis in solids, Degenerate parabolic equations, degenerate PDE, Analysis of PDEs (math.AP)
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