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The Riemann Problem for an Inhomogeneous Conservation Law Without Convexity

1997; Society for Industrial and Applied Mathematics; Volume: 28; Issue: 1 Linguagem: Inglês

10.1137/s003614109427446x

1095-7154

Carlo Sinestrari,

Cosmology and Gravitation Theories

The paper studies the Riemann problem for a conservation law with a source term and a nonconvex f{l}ux-function. The complete solution is provided in the case when the f{l}ux has one inf{l}ection 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 f{l}ux has more than one inf{l}ection point, there may be shocks vanishing in finite time, in contrast to the case when the f{l}ux is convex.