Rarefaction wave

Summary

A rarefaction wave is a continuous solution of a conservation law that spreads out from a point like a fan. In the fan, the unknown takes every value between two states. It is self-similar: it depends only on $x/t$. It is the admissible solution when the characteristics on the two sides of a jump move apart. In that case a shock wave would violate the entropy condition. Together with shocks and contact discontinuities, rarefaction waves are the building blocks of solutions of the Riemann problem. See the definition.