Relaxation limit for hyperbolic systems in chromatography

This paper is concerned with a $2n \times 2n$ nonlinear system which arises in chromatography. The global existence of solutions $(u^{\tau}_{i},v^{\tau}_{i})$ in $L^{\infty}$ space for a Cauchy problem with initial data is obtained for any fixed $\tau > 0$, and the convergence of $(u^{\tau}_{i},v^{\tau}_{i})$ to its equilibrium state $(u_{i},v_{i})$, governed by a limit system is proved for the case $n=2$ by using the compensated compactness coupled with the framework of Tzavaras (1999).