Modeling and analysis of adsorption and adsorption hysteresis

The simplest model of adsorption is a scalar conservation law with a convex, concave, or sigmoid flux functional. Appropriately the analysis of solutions proceeds in very weak spaces such as L¹. The hysteresis phenomenon in adsorption is caused by different rates of adsorption and desorption.  We discuss mathematical models of adsorption hysteresis based on auxiliary differential equations which lead to interesting well-posedness results.