Departamento de Matematicas, Universidad de Sonora, Calle Rosales y Blvd Luis Encinas, s/n, 83000, Hermosillo, Sonora, Mexico
Copyright © 2009 Antonio Olivas Martinez and Georgy A. Omel'yanov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider the Riemann problem for the Hopf equation with concave-convex flux functions. Applying the weak asymptotics method we construct a uniform in time description for the Cauchy data evolution and show that the use of this method implies automatically the appearance of the Oleinik E-condition.