Abstract and Applied Analysis
Volume 2009 (2009), Article ID 350762, 26 pages
doi:10.1155/2009/350762
Research Article

Smooth Approximations of Global in Time Solutions to Scalar Conservation Laws

V. G. Danilov1 and D. Mitrovic2

1Department of Mathematics, Moscow Technical University of Communication and Informatics, Aviamotornaya 8a, 111024 Moscow, Russia
2Faculty of Mathematics, University of Montenegro, Cetinjski put bb, 81000 Podgorica, Montenegro

Received 16 August 2008; Accepted 15 January 2009

Academic Editor: Samuel Shen

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.

Abstract

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.