# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Convex hulls, sticky particle dynamics and pressure-less gas system. (English) Zbl 1153.76062
Summary: We introduce a new condition which extends the definition of sticky particle dynamics to the case of discontinuous initial velocities ${u}_{0}$ with negative jumps. We show the existence of a stochastic process and a forward flow $\phi$ satisfying ${X}_{s+t}=\phi \left({X}_{s},t,{P}_{s},{u}_{s}\right)$ and $d{X}_{t}=E\left[{u}_{0}\left({X}_{0}\right)/{X}_{t}\right]dt$, where ${P}_{s}=P{X}_{s}^{-1}$ is the law of ${X}_{s}$ and ${u}_{s}\left(x\right)=E\left[{u}_{0}\left({X}_{0}\right)/{X}_{s}=x\right]$ is the velocity of particle $x$ at time $s\ge 0$. Results on the flow characterization and Lipschitz continuity are also given. Moreover, the map $\left(x,t\right)↦M\left(x,t\right):=P\left({X}_{t}\le x\right)$ is the entropy solution of a scalar conservation law ${\partial }_{t}M+{\partial }_{x}\left(A\left(M\right)\right)=0$, where the flux $A$ represents the particles momentum, and ${P}_{t},{u}_{t},t>0$ is a weak solution of the pressure-less gas system of equations of initial datum ${P}_{0},{u}_{0}$.
##### MSC:
 76T15 Dusty-gas two-phase flows 76M35 Stochastic analysis (fluid mechanics) 60H30 Applications of stochastic analysis 60H15 Stochastic partial differential equations