THE RIEMANN PROBLEM FOR AN INHOMOGENEOUS CONSERVATION LAW WITHOUT CONVEXITY

The paper studies the Riemann problem for a conservation law with a so urce term and a nonconvex flux-function The complete solution is provi ded in the case when the flux has one inflection point and the Riemann states are stationary states of the source term. For small times, the structure of the solutions is similar to the homogeneous case. As the time increases, the size of the shocks may decrease under the action of the source, while rarefaction waves tend to traveling waves. It is also proved that if the flux has more than one inflection point, there may be shocks vanishing in finite time, in contrast to the case when the flux is convex.