Jx. Hu, THE RIEMANN PROBLEM FOR A RESONANT NONLINEAR-SYSTEM OF CONSERVATION-LAWS WITH DIRAC-MEASURE SOLUTIONS, Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 128, 1998, pp. 81-94
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.