Mass, momentum and energy conservation laws in zero-pressure gas dynamics and delta-shocks

For one-dimensional system of zero-pressure gas dynamics, we derive the balance laws describing mass, momentum and energy transport from the area outside the δ-shock wave front onto its front. It is proved that the total mass and momentum of area outside δ-shock wave front and the the δ-shock wave f...

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Bibliographic Details
Published in:Applicable analysis 2011-11, Vol.90 (11), p.1677-1689
Main Authors: Nilsson, B., Shelkovich, V.M.
Format: Article
Language:English
Subjects:
Cauchy problem
Cauchy problems
Conservation laws
Dynamical systems
Dynamics
Energy
Energy conservation
Energy conservation law
Gas dynamics
Kinetic energy
Primary 35L65
Secondary 35L67, 76L05
TECHNOLOGY
TEKNIKVETENSKAP
the Rankine-Hugoniot conditions
Transport
transportation and concentration processes
Vågor och signaler
Wave fronts
Waves and Signals
zero-pressure gas dynamics
δ-shocks
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Description
Summary:For one-dimensional system of zero-pressure gas dynamics, we derive the balance laws describing mass, momentum and energy transport from the area outside the δ-shock wave front onto its front. It is proved that the total mass and momentum of area outside δ-shock wave front and the the δ-shock wave front are conserved, while the kinetic energy of the area outside the δ-shock wave front and total kinetic energy are decreasing quantities. It is also proved that if the kinetic energy is conserved then the Cauchy problem cannot have any nontrivial δ-shock wave type solution.
ISSN:0003-6811
1563-504X
1563-504X
DOI:10.1080/00036810903569515