The perturbed Riemann problem and delta contact discontinuity in chromatography equations

In this paper, we discuss the perturbed Riemann problem for the nonlinear chromatography equations. The solutions to the problem are constructed with the method of the splitting delta function. In solutions, we find another kind of delta contact discontinuity on which both state variables simultaneously contain the Dirac delta functions. It is quite different from the previous ones on which only one state variable contains the Dirac delta function. This phenomenon is also predicted theoretically by Mazzotti (2009) and Mazzotti et al. (2010). Moreover, by studying the limits of the solutions as the perturbed parameter ε→0ε→0, it can be found that the Riemann solutions are stable for such perturbations with the initial data.