Long-time behaviors and stability of entropy solutions for linearly   degenerate hyperbolic systems of rich type
  We show that in one space dimension, a linearly degenerate hyperbolic system of rich type admits exact traveling wave solutions if the initial data are Riemann type outside of a space interval. In a particular case of the system including physical models, we prove the convergence of entropy solutions to traveling waves in the $L^1$ norm as the time goes to infinity. The traveling waves are determined explicitly in terms of the initial data and the system. We also obtain the stability of entropy solutions in $L^1$. 
Yue-Jun Peng and Yong-Fu Yang
math.AP math-ph math.MP