Convex hulls, Sticky particle dynamics and Pressure-less gas system
Annales mathématiques Blaise Pascal, Tome 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
Mots-clés : Convex hull, sticky particles, forward flow, stochastic differential equation, scalar conservation law, pressure-less gas system, Hamilton-Jacobi equation
Moutsinga, Octave 1

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

[1] Brenier, Y.; Grenier, E. Sticky particles and scalar conservation laws, Siam. J. Numer. Anal., Volume 35 (1998), pp. 2317-2328 (No 6) | DOI | MR | Zbl

[2] Dafermos, C. M. Polygonal approximations of solutions of the initial value problem for a conservation law, Journal of Mathematical Analysis and Appl., Volume 38 (1972), pp. 33-41 | DOI | MR | Zbl

[3] Dermoune, A. Probabilistic interpretation for system of conservation law arising in adhesion particle dynamics, C. R. Acad. Sci. Paris, Volume tome 5 (1998), pp. 595-599 | MR | Zbl

[4] Dermoune, A.; Moutsinga, O. Generalized variational principles, Séminaire de Probabilités XXXVI, Lect. Notes in Math., Volume 1801 (2003), pp. 183-193 | EuDML | Numdam | MR | Zbl

[5] E, W.; Rykov, Yu. G.; Sinai, Ya. G. Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics, Com. Math. Phys., Volume 177 (1996), pp. 349-380 | DOI | MR | Zbl

[6] Moutsinga, O. Equations de gaz sans pression avec une distribution initiale de Radon (2002) Technical report (Preprint)

[7] Moutsinga, O. Probabilistic approch of sticky particles and pressure-less gas system, Univ. Sciences Tech. Lille (2003) (Ph. D. Thesis)

[8] Zeldovich, Ya. B. Gravitational instability; an approximation theory for large density perturbations, Astron. Astrophys, Volume 5 (1970), pp. 84-89

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