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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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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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creator	Nilsson, B. Shelkovich, V.M.
description	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.
doi_str_mv	10.1080/00036810903569515
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source	Taylor and Francis Science and Technology Collection
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
title	Mass, momentum and energy conservation laws in zero-pressure gas dynamics and delta-shocks
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