Comptes Rendus
Propagation of chaos for pressureless gas equations with viscosity
Comptes Rendus. Mathématique, Volume 335 (2002) no. 11, pp. 935-940.

We use A.S. Sznitman ideas of probabilistic phenomenon of propagation of chaos for Burgers equation, and we derive the existence and uniqueness of a weak solution of the following system of pressureless gas equations with viscosity:

(𝒮){ tρ+ x(uρ)=1 2 2 2 xρ, t(uρ)+ x(u 2 ρ)=1 2 2 2 x(uρ),ρ(dx,t)ρ(dx,0),u(x,t)ρ(dx,t)u 0 (x)ρ(dx,0) weakly as t0 + .

Dans cette Note on utilise les idées de A.S. Sznitman dans son étude de la propagation du chaos probabiliste pour l'équation de Burgers, et on obtient l'existence et l'unicité d'une solution faible au système (𝒮) de gaz sans pression avec viscosité cité dans l'abstract.

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DOI: 10.1016/S1631-073X(02)02602-X
Azzouz Dermoune 1

1 Laboratoire de probabilités et statistique, UFR de mathématiques, USTL, bât. M2, 59655 Villeneuve d'Ascq cedex, France
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Azzouz Dermoune. Propagation of chaos for pressureless gas equations with viscosity. Comptes Rendus. Mathématique, Volume 335 (2002) no. 11, pp. 935-940. doi : 10.1016/S1631-073X(02)02602-X. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02602-X/

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[5] D.W. Stroock; S.R.S. Varadhan Mutidimensional Diffusion Processes, Springer, New York, 1979

[6] A.S. Sznitman A propagation of chaos results for Burgers' equation, Probab. Theory Related. Fields, Volume 71 (1986), pp. 581-613

[7] A.S. Sznitman, Topics in propagation of chaos, École d'Été de Probabilités de Saint-Flours XIX, 1989

[8] A.S. Sznitman Equations de type Boltzmann spatialement homogènes, Z. Wahrscheinlichkeitstheor. Verw. Gebiete, Volume 66 (1984), pp. 559-592

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