Convex hulls, Sticky particle dynamics and Pressure-less gas system
Annales mathématiques Blaise Pascal, Volume 15 (2008) no. 1, pp. 57-80.

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 φ satisfying X s+t =φ(X s ,t,P s ,u s ) and dX t =E[u 0 (X 0 )/X t ]dt, where P s =PX s -1 is the law of X s and u s (x)=E[u 0 (X 0 )/X s =x] is the velocity of particle x at time s0. Results on the flow characterization and Lipschitz continuity are also given.

Moreover, the map (x,t)M(x,t):=P(X t x) is the entropy solution of a scalar conservation law t M+ x (A(M))=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 .

DOI: 10.5802/ambp.239
Classification: 52A10,  52A22,  60G44,  60H10,  60H30
Keywords: Convex hull, sticky particles, forward flow, stochastic differential equation, scalar conservation law, pressure-less gas system, Hamilton-Jacobi equation
Octave Moutsinga 1

1 Université des Sciences et Techniques de Masuku Faculté des Sciences - Dpt Mathématiques et Informatique BP 943 Franceville, Gabon.
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Octave Moutsinga. Convex hulls, Sticky particle dynamics and Pressure-less gas system. Annales mathématiques Blaise Pascal, Volume 15 (2008) no. 1, pp. 57-80. doi : 10.5802/ambp.239. https://ambp.centre-mersenne.org/articles/10.5802/ambp.239/

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