Diffusion in porous media with hysteresis and bounded speed of propagation
Chiara Gavioli, Pavel Krej\v{c}\'i
TL;DR
This paper demonstrates that moisture propagation in porous media with hysteresis and nonlinear flux-pressure relations has a bounded speed of propagation, establishing conditions for solutions and providing an upper speed bound.
Contribution
It introduces a model showing bounded propagation speed in porous media with hysteresis, extending previous Darcy law models to include hysteresis effects.
Findings
Bounded speed of moisture propagation established
Conditions for existence and uniqueness of solutions specified
Upper bound for propagation speed derived
Abstract
It is shown that the problem of moisture propagation in porous media with a nonlinear relation between the mass flux and the pressure gradient as a counterpart of the Darcy law exhibits the property of bounded speed of propagation even in the case of a hysteresis relation between the capillary pressure and the moisture content. The paper specifies conditions for existence and uniqueness of solutions, and provides an upper bound for the moisture propagation speed.
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