On Some Properties of Kinetic and Hydrodynamic Equations for Inelastic Interactions

By A. Bobylev, José Antonio Carrillo, Irene M. Gamba. 2000

240 citations recorded by the source corpus.

Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Geophysics

View Paper: https://www.semanticscholar.org/paper/6148ef4258fad4298c6c45fc5df09ec3d1d7c5f2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Atomic and Molecular Physics, and Optics

In Geophysics

Citations in the corpus

On the Boltzmann Equation for Diffusively Excited Granular Media (2003, methodology): “The same problem was also studied in [9] and in [6], for a different kind of interactions, namely the Maxwell pseudo-particle model [5, 26, 27], by methods of expansions and the Fourier transforms, respectively.”
Mathematical tools for kinetic equations (2004, background): “For instance recent interest has been to understand inelastic collisions, because such models arise in some regimes of granular flows; see Bobylev, Carillo and Gamba [22], Toscani [112], and Benedetto et al.”
Fractional Diffusion Limit for Collisional Kinetic Equations (2008, background): “Dissipative collision mechanisms in granular gases can also produce power law tails: see for instance [11] for the so-called “inelastic Maxwell model” introduced in [4].”
Contractive Probability Metrics and Asymptotic Behavior of Dissipative Kinetic Equations (2007, background): “Although a formulation of the collision operator in strong form can be done [20], we will not write it here since it will be never used.”
Chapter 2 – A Review of Mathematical Topics in Collisional Kinetic Theory (2002, methodology): “Further clarification is still badly needed; an attempt is done in [86] for the simplified pseudo-Maxwellian model.”
On a Kinetic Model for a Simple Market Economy (2004, result): “Finally we remark that the formation of power law tails for large times in the present kinetic model is in accord with the overpopulated energy tails for the Boltzmann equation for a dissipative granular Maxwellian gas [ 3 , 1, 9, 10].”
Long-Time Asymptotics of Kinetic Models of Granular Flows (2004, background): “In addition, unlike the Boltzmann models for granular flows (see the discussion in [ 5 ]), these equations exhibit similarity solutions, which are in general of noticeable importance for understanding the cooling process of the granular flow, and eventually for constructing reasonable macroscopic eq”