International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 101647, 16 pages
doi:10.1155/2009/101647

Uniform in time description for weak solutions of the Hopf equation with nonconvex nonlinearity

Antonio Olivas Martinez and Georgy A. Omel'yanov

Departamento de Matematicas, Universidad de Sonora, Calle Rosales y Blvd Luis Encinas, s/n, 83000, Hermosillo, Sonora, Mexico

Abstract

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.