The multiplication of distributions in the study of delta shock wave for the nonlinear chromatography system

In the frame of $\alpha ?$solutions defined in the setting of distributional products, the discontinuous solutions to the Riemann problem for a nonlinear chromatography system are constructed. All the discontinuous solutions are obtained within a convenient space of distributions including discontinuous functions and Dirac delta measures. The constructed $\alpha ?$solutions are reasonable in comparison with the known results by using other techniques.