Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

The Riemann problem for a resonant nonlinear system of conservation laws with Dirac-measure solutions*

Jiaxin Hua1

a1 Young Scientists Laboratory of Mathematical Physics, Wuhan Institute of Mathematical Sciences, Academia Sinica, P.O. Box 71007, Wuhan 430071, P.R. China

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

(Received July 23 1996)

(Revised January 03 1997)

Footnotes

* This work was supported by CYNSY.