Geodesic
On measure solutions to the Zero-pressure gas model and their uniqueness
Mathematica Bohemica, Tome 127 (2002) no. 2, pp. 265-273
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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.
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.
DOI : 10.21136/MB.2002.134173
Classification : 35L65, 35L80, 70F16, 76N10, 76N15
Keywords: zero-pressure gas dynamics; measure solutions uniqueness; entropy condition; cohesion condition; generalized characteristics 
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Li, Jiequan; Warnecke, Gerald. On measure solutions to the Zero-pressure gas model and their uniqueness. Mathematica Bohemica, Tome 127 (2002) no. 2, pp. 265-273. doi: 10.21136/MB.2002.134173

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