Hysteresis in porous media

Abstract: We propose a model for fluid diffusion in partially saturated porous media taking into account saturation-dependent permeability as well as hysteresis effects in the pressure saturation relation. The resulting mathematical problem leads to a diffusion equation for the pressure in an N-dimensional domain with a Preisach hysteresis operator under the time derivative and in the diffusion coefficient. The problem is doubly degenerate in the sense that the saturation range is bounded, and no a priori control of the time derivative of the pressure is available. We discuss the conditions for existence and uniqueness of a solution to the problem with or without gravity effects in appropriate function spaces, as well as the question of bounded speed of propagation. This is a joint work with Chiara Gavioli.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)