Smooth Approximations of Global in Time Solutions to Scalar Conservation LawsReport as inadecuate




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Abstract and Applied AnalysisVolume 2009 2009, Article ID 350762, 26 pages

Research Article

Department of Mathematics, Moscow Technical University of Communication and Informatics, Aviamotornaya 8a, 111024 Moscow, Russia

Faculty 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 aredescribed as well. In order to solve the problem, we use and further developthe weak asymptotic method, recently introduced technique for investigating nonlinear waves interactions.





Author: V. G. Danilov and D. Mitrovic

Source: https://www.hindawi.com/



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