THE RIEMANN PROBLEM FOR A RESONANT NONLINEAR-SYSTEM OF CONSERVATION-LAWS WITH DIRAC-MEASURE SOLUTIONS

The Riemann problem for a resonant nonlinear system of conservation la ws is considered here. The Riemann solution was constructed by employi ng the viscosity approximation approach. One kind of new discontinuity , which is called the Dirac-contact wave, appeared in the Riemann solu tion. Because the strict hyperbolicity as well as the genuine nonlinea rity of the system considered failed, the solution we obtained in this paper is not unique for some initial data. An additional condition wa s explored to guarantee the uniqueness of the Riemann problem.