The Richards equation with hysteresis and degenerate capillary pressure

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We study the Richards equation with a dynamic capillary pressure, including hysteresis. We provide existence and approximation results for degenerate capillary pressure curves p c, treating two cases. In the first case, the permeability function k can be degenerate, but the initial saturation does not take the critical values. In the second case, the permeability function k is strictly positive, but the capillary pressure function can be multi-valued. In both cases, the degenerate behavior of p c leads to the physically desired uniform bounds for the saturation variable. Our approach exploits maximum principles and relies on the corresponding uniform bounds for pressure and saturation. A new compactness result for the saturation variable allows to take limits in nonlinear terms. The solution concept uses tools of convex analysis. © 2012 Elsevier Inc.




Schweizer, B. (2012). The Richards equation with hysteresis and degenerate capillary pressure. Journal of Differential Equations, 252(10), 5594–5612.

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