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Advances in Mathematical Physics
Volume 2016, Article ID 1783689, 12 pages
Research Article

Interactions of Delta Shock Waves for Zero-Pressure Gas Dynamics with Energy Conservation Law

1The Basic Department, The First Aeronautic Institute of the Air Force, Xinyang 464000, China
2College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, China

Received 1 April 2016; Accepted 15 May 2016

Academic Editor: Ming Mei

Copyright © 2016 Wei Cai and Yanyan Zhang. 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 study the interactions of delta shock waves and vacuum states for the system of conservation laws of mass, momentum, and energy in zero-pressure gas dynamics. The Riemann problems with initial data of three piecewise constant states are solved case by case, and four different configurations of Riemann solutions are constructed. Furthermore, the numerical simulations completely coinciding with theoretical analysis are shown.