On the one-dimensional Boltzmann equation for granular flows
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 35 (2001) no. 5, p. 899-905

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

Classification:  82C40,  76T25
Keywords: inelastic collisions, granular media, Boltzmann equation
@article{M2AN_2001__35_5_899_0,
     author = {Benedetto, Dario and Pulvirenti, Mario},
     title = {On the one-dimensional Boltzmann equation for granular flows},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {5},
     year = {2001},
     pages = {899-905},
     zbl = {1044.82012},
     mrnumber = {1866273},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2001__35_5_899_0}
}
Benedetto, Dario; Pulvirenti, Mario. On the one-dimensional Boltzmann equation for granular flows. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 35 (2001) no. 5, pp. 899-905. http://www.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 0654.76073

[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. | Numdam | Zbl 0888.73006

[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 1011.82019

[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). | 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). | Numdam | MR 466992 | Zbl 0336.35069

[6] G. Toscani, One-dimensional kinetic models of granular flows. Math. Model. Numer. Anal. 34 (2000) 1277-1291. | Numdam | Zbl 0981.76098