Existence of global Lp solutions to a system of conservation laws in chromatography with geometry effects

In this paper, we give the global existence of Lp bounded entropy solutions for the Cauchy problem of a system of conservation laws in chromatography with geometry effects. The main difficulty lies in establishing the Lp estimate of the viscosity solutions because the initial data may not be L∞ bounded and the principle of invariant regions developed by Conley-Chuey-Smoller is invalid here. We obtain the existence of the global weak solutions using the compensated compactness method and BV estimates on viscosity solutions.