Copyright © 2009 V. G. Danilov and D. Mitrovic. 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 construct global smooth approximate solution to a scalar conservation law with arbitrary smooth monotonic initial data. Different kinds of singularities interactions which arise during the evolution of the initial data are
described as well. In order to solve the problem, we use and further develop
the weak asymptotic method, recently introduced technique for investigating nonlinear waves interactions.