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Propagation trajectorielle du chaos pour les lois de conservation scalaire

Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 1686)

Résumé

A l'aide d'un problème de martingales, nous donnons une interprétation probabiliste trajectorielle de la solution d'une équation cinétique associée aux lois de conservation scalaire. Puis nous montrons que l'unique solution de ce problème est la limite au sens de la propagation du chaos d'une suite de lois de systèmes de particules en interaction, étendant ainsi un résultat obtenu par Perthame et Pulvirenti [2] pour les marginales en temps.

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Références

  1. P.A. Meyer, Probabilités et Potential. Hermann, 1966.

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  2. B. Perthame and M. Pulvirenti. On some large systems of random particles which approximate scalar conservation laws. Asymt. Anal., 10(3):263–278, 1995.

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  3. B. Perthame and E. Tadmor. A kinetic equation with kinetic entropy functions for scalar conservation laws. Comm. Math. Phys., 136:501–517, 1991.

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  4. A.S. Sznitman. Equations de type de Boltzmann spatialement homogènes. Z. Warsch. Verw. Geb., 66:559–592, 1984.

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© 1998 Springer-Verlag

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Jourdain, B. (1998). Propagation trajectorielle du chaos pour les lois de conservation scalaire. In: Azéma, J., Yor, M., Émery, M., Ledoux, M. (eds) Séminaire de Probabilités XXXII. Lecture Notes in Mathematics, vol 1686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101759

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  • DOI: https://doi.org/10.1007/BFb0101759

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64376-0

  • Online ISBN: 978-3-540-69762-6

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