Summary: ``The boundary entropy inequality problem of simplified chromatography equation was discussed by using entropy flux pair and the viscosity vanishing method. Firstly, by judging whether the solutions of the initial value problem of the chromatography equation satisfied the boundary entropy inequality, we gave the interaction of the elementary waves on the boundary, and then gave the global solutions for the initial boundary value problem of the chromatography equation. Secondly, the correctness of the theoretical analysis for the initial boundary value problem was verified by numerical simulation.''