Strong Stability with respect to weak limit for a Hyperbolic System arising from Gas Chromatography

We investigate a system related to a particular isothermal gas-solid chromatography process, called “Pressure Swing Adsorption”, with two species and instantaneous exchange kinetics. This system presents the particularity to have a linearly degenerate eigenvalue: this allows the velocity of the gaseous mixture to propagate high frequency waves. In case of smooth concentrations with a general isotherm, we prove L stability for concentrations with respect to weak limits of the inlet boundary velocity. Using the Front Tracking Algorithm (FTA), we prove a similar result for concentrations with bounded variation (BV) under some convex assumptions on the isotherms. In both cases we show that high frequency oscillations with large amplitude of the inlet velocity can propagate without affecting the concentrations.