Viscous Rarefaction Waves by Tai-ping Liu and Shih-hsien Yu

A rarefaction wave for system of viscous conservation laws induces strong coupling of waves pertaining to different characteristic fields. For the characteristic field pertaining to the rarefaction wave, there are the nonlinear hyperbolic, linear in time, and the parabolic, sub-linear in time, dissipations. We study the quantitative properties of the waves propagating around the rarefaction wave. Our analysis depends on the explicit informations on the wave coupling obtained through the Hopf-Cole transformation for the Burgers equation, and an inner-outer expansion for waves propagating between the characteristic directions.