Mass, momentum and energy conservation laws in zero-pressure gas dynamics and δ-shocks: II

We study δ-shocks in a one-dimensional system of zero-pressure gas dynamics. In contrast to well-known papers (see References) this system is considered in the form of mass, momentum and energy conservation laws. In order to define such singular solutions, special integral identities are introduced...

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Bibliographic Details
Published in:Applicable analysis 2011-05, Vol.90 (5), p.831-842
Main Authors: Nilsson, B., Rozanova, O.S., Shelkovich, V.M.
Format: Article
Language:English
Subjects:
Dynamical systems
Dynamics
Energy conservation law
Fysik
Gas dynamics
Integrals
Internal energy
Kinetic energy
NATURAL SCIENCES
NATURVETENSKAP
Physics
Primary 35L65
Secondary 35L67
transportation and concentration processes of mass, momentum and energy
Wave fronts
zero-pressure gas dynamics
δ-shocks, the Rankine-Hugoniot conditions
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Summary:We study δ-shocks in a one-dimensional system of zero-pressure gas dynamics. In contrast to well-known papers (see References) this system is considered in the form of mass, momentum and energy conservation laws. In order to define such singular solutions, special integral identities are introduced which extend the concept of classical weak solutions. Using these integral identities, the Rankine-Hugoniot conditions for δ-shocks are obtained. It is proved that the mass, momentum and energy transport processes between the area outside the of one-dimensional δ-shock wave front and this front are going on such that the total mass, momentum and energy are independent of time, while the mass and energy concentration processes onto the moving δ-shock wave front are going on. At the same time the total kinetic energy transforms into total internal energy.
ISSN:0003-6811
1563-504X
1563-504X
DOI:10.1080/00036811.2010.524156