Convergence results for some conservation laws with a reflux boundary condition and a relaxation term arising in chemical engineering

This paper deals with a system of 2N semilinear transport equations with a boundary condition of imposed flux. The right-hand side models some kinetic exchange between two phases. It is thus a stiff term involving a small parameter which will tend to 0. Using compensated compactness, one proves, under some assumptions on the flux, that the solution to this system converges to a solution to a system of N quasilinear equations, a solution which satisfies a set of entropy inequalities. Thus the reflux boundary condition for the quasi-linear system is given a meaning.