A Theoretical Model of Hysteresis and Dynamic Effects in the Capillary Relation for Two-phase Flow in Porous Media

By A. Yu. Beliaev, S. Majid Hassanizadeh. 2001

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Two-phase flow equations with outflow boundary conditions in the hydrophobic–hydrophilic case (2010, background): “We remark that more general models can also be studied, of particular interest are hysteresis relations [5], [18].”
Dynamic Effect in the Capillary Pressure–Saturation Relationship and its Impacts on Unsaturated Flow (2002, methodology): “Saturation profiles at time t 12 h, for various values of .content, and an iterative procedure is then followed (see Beliaev and Hassanizadeh, 2001).”
A global existence result for the equations describing unsaturated flow in porous med (2010, unknown): “For the nonlinear model from [16] there are only papers [4] and [5], where the non-degeneracy was supposed and existence is local in time.”