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
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: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {899--905},
     year = {2001},
     publisher = {EDP Sciences},
     volume = {35},
     number = {5},
     mrnumber = {1866273},
     zbl = {1044.82012},
     language = {en},
     url = {https://www.numdam.org/item/M2AN_2001__35_5_899_0/}
}
TY  - JOUR
AU  - Benedetto, Dario
AU  - Pulvirenti, Mario
TI  - On the one-dimensional Boltzmann equation for granular flows
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 2001
SP  - 899
EP  - 905
VL  - 35
IS  - 5
PB  - EDP Sciences
UR  - https://www.numdam.org/item/M2AN_2001__35_5_899_0/
LA  - en
ID  - M2AN_2001__35_5_899_0
ER  - 
%0 Journal Article
%A Benedetto, Dario
%A Pulvirenti, Mario
%T On the one-dimensional Boltzmann equation for granular flows
%J ESAIM: Modélisation mathématique et analyse numérique
%D 2001
%P 899-905
%V 35
%N 5
%I EDP Sciences
%U https://www.numdam.org/item/M2AN_2001__35_5_899_0/
%G en
%F M2AN_2001__35_5_899_0
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. https://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

[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 | EuDML

[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). | Numdam | EuDML

[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 | Zbl | MR | EuDML

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