On measure solutions to the Zero-pressure gas model and their uniqueness

Jiequan Li; Gerald G. Warnecke

Mathematica Bohemica (2002)

  • Volume: 127, Issue: 2, page 265-273
  • ISSN: 0862-7959

Abstract

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The system of zero-pressure gas dynamics conservation laws describes the dynamics of free particles sticking under collision while mass and momentum are conserved. The existence of such solutions was established some time ago. Here we report a uniqueness result that uses the Oleinik entropy condition and a cohesion condition. Both of these conditions are automatically satisfied by solutions obtained in previous existence results. Important tools in the proof of uniqueness are regularizations, generalized characteristics and flow maps. The solutions may contain vacuum states as well as singular measures.

How to cite

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Li, Jiequan, and Warnecke, Gerald G.. "On measure solutions to the Zero-pressure gas model and their uniqueness." Mathematica Bohemica 127.2 (2002): 265-273. <http://eudml.org/doc/249041>.

@article{Li2002,
abstract = {The system of zero-pressure gas dynamics conservation laws describes the dynamics of free particles sticking under collision while mass and momentum are conserved. The existence of such solutions was established some time ago. Here we report a uniqueness result that uses the Oleinik entropy condition and a cohesion condition. Both of these conditions are automatically satisfied by solutions obtained in previous existence results. Important tools in the proof of uniqueness are regularizations, generalized characteristics and flow maps. The solutions may contain vacuum states as well as singular measures.},
author = {Li, Jiequan, Warnecke, Gerald G.},
journal = {Mathematica Bohemica},
keywords = {zero-pressure gas dynamics; measure solutions uniqueness; entropy condition; cohesion condition; generalized characteristics; entropy condition; cohesion condition; generalized characteristics},
language = {eng},
number = {2},
pages = {265-273},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On measure solutions to the Zero-pressure gas model and their uniqueness},
url = {http://eudml.org/doc/249041},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Li, Jiequan
AU - Warnecke, Gerald G.
TI - On measure solutions to the Zero-pressure gas model and their uniqueness
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 2
SP - 265
EP - 273
AB - The system of zero-pressure gas dynamics conservation laws describes the dynamics of free particles sticking under collision while mass and momentum are conserved. The existence of such solutions was established some time ago. Here we report a uniqueness result that uses the Oleinik entropy condition and a cohesion condition. Both of these conditions are automatically satisfied by solutions obtained in previous existence results. Important tools in the proof of uniqueness are regularizations, generalized characteristics and flow maps. The solutions may contain vacuum states as well as singular measures.
LA - eng
KW - zero-pressure gas dynamics; measure solutions uniqueness; entropy condition; cohesion condition; generalized characteristics; entropy condition; cohesion condition; generalized characteristics
UR - http://eudml.org/doc/249041
ER -

References

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