no. 5
On the one-dimensional Boltzmann equation for granular flows
ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 5, pp. 899-905.

We consider a Boltzmann equation for inelastic particles on the line and prove existence and uniqueness for the solutions.

Classification : 82C40, 76T25
Mots clés : inelastic collisions, granular media, Boltzmann equation 
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     author = {Benedetto, Dario and Pulvirenti, Mario},
     title = {On the one-dimensional {Boltzmann} equation for granular flows},
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     pages = {899--905},
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     number = {5},
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Benedetto, Dario; Pulvirenti, Mario. On the one-dimensional Boltzmann equation for granular flows. ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 5, pp. 899-905. http://archive.numdam.org/item/M2AN_2001__35_5_899_0/

[1] L. Arkeryd, Existence theorems for certain kinetic equations and large data. Arch. Rational Mech. Anal. 103 (1988) 139-149. | Zbl

[2] D. Benedetto, E. Caglioti and M. Pulvirenti, A kinetic equation for one-dimensional granular media. RAIRO Modél. Math. Anal. Numér. 31 (1997) 615-641. | EuDML | Numdam | Zbl

[3] D. Benedetto, E. Caglioti and M. Pulvirenti, A one-dimensional Boltzmann equation with inelastic collisions. Rend. Sem. Mat. Fis. Milano LXVII (1997) 169-179. | Zbl

[4] J.-M. Bony, Solutions globales bornées pour les modèles discrets de l'équation de Boltzmann en dimension 1 d'espace, in Actes Journées Équ. Dériv. Part. 16, St.-Jean-de-Monts (1987). | EuDML | Numdam

[5] L. Tartar, Existence globale pour un système hyperbolique semi-linéaire de la théorie cinétique des gaz, in Séminaire Goulaouic-Schwartz 1975-76, Équat. Dériv. Part. Anal. Fonct., Exposé I, École Polytechnique, Palaiseau (1976). | EuDML | Numdam | MR | Zbl

[6] G. Toscani, One-dimensional kinetic models of granular flows. Math. Model. Numer. Anal. 34 (2000) 1277-1291. | EuDML | Numdam | Zbl