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MATHEMATICA BOHEMICA, Vol. 127, No. 2, pp. 265-273 (2002)
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# On measure solutions to the Zero-pressure gas model and their uniqueness

## Jiequan Li, Gerald Warnecke

* Jiequan Li*, Institute of Mathematics, Academia Sinica, Beijing, 100080, P. R. China, e-mail: ` jiequan@math.sinica.edu.tw`; * Gerald Warnecke*, Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, 39016 Magdeburg,Germany, e-mail: ` gerald.warnecke@mathematik.uni-magdeburg.de`

**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.

**Keywords:** zero-pressure gas dynamics, measure solutions uniqueness, entropy condition, cohesion condition, generalized characteristics

**Classification (MSC2000):** 35L65, 35L80, 70F16, 76N10

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