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 wi th a boundary condition of imposed flux. The right-hand side models so me kinetic exchange between two phases. It is thus a stiff term involv ing a small parameter which will tend to 0. Using compensated compactn ess, one proves, under some assumptions on the flux, that the solution to this system converges to a solution to a system of N quasilinear e quations, a solution which satisfies a set of entropy inequalities. Th us the reflux boundary condition for the quasi-linear system is given a meaning.