6 citations · 18 across the 9 of their papers we have counts for
9 papers
Four collapsing one-dimensional particles: a dynamical system approach of the spherical billiard reduction
Roberto Castorrini, Théophile Dolmaire
We consider a system of four one-dimensional inelastic hard spheres evolving on the real line , and colliding according to a scattering law characterized by a fixed res…
Boltzmann-Grad limit for the inelastic Lorentz gas: Part I. Existence, uniqueness, and rigorous derivation via weak convergence
Théophile Dolmaire, Alessia Nota
In this paper we provide a rigorous derivation of the inelastic linear Boltzmann equation, in the Boltzmann-Grad limit, from a dissipative, random, Lorentz gas in arbitrary dimensi…
The global attractor of the inelastic linear Boltzmann equation in a gravity field for Maxwell molecules
Théophile Dolmaire, Nicola Miele, Alessia Nota
In this article we consider the linear inelastic Boltzmann equation in presence of a uniform and fixed gravity field, in the case of Maxwell molecules. We first obtain a well-posed…
On the local Maxwellians solving the Boltzmann equation with boundary condition
Théophile Dolmaire
We derive the expressions of the local Maxwellians that solve the Boltzmann equation in the interior of an open domain. We determine which of these local Maxwellians satisfy the Bo…
One-dimensional inelastic collapse of four particles: asymmetric collision sequences and spherical billiard reduction
Théophile Dolmaire, Eleni Hübner-Rosenau
We consider a one-dimensional system of four inelastic hard spheres, colliding with a fixed restitution coefficient , and we study the inelastic collapse phenomenon for such a p…
Properties of some dynamical systems for three collapsing inelastic particles
Théophile Dolmaire, Juan J. L. Velázquez
In this article we continue the study of the collapse of three inelastic particles in dimension , complementing the results we obtained in its companion paper. We focus o…
An Alexander-like theorem for a particle model with inelastic collisions
Théophile Dolmaire, Juan J. L. Velázquez
We consider a finite system of hard spheres that collide inelastically according to a particular model, losing a fixed amount of kinetic energy at each collision. We develop the th…
Collapse of inelastic hard spheres in dimension
Théophile Dolmaire, Juan J. L. Velázquez
We investigate the collapse of three inelastic particles in dimension . We obtain general results of convergence and asymptotics concerning the variables of the dynamical…
About Lanford's theorem in the half-space with specular reflection
Théophile Dolmaire
The present article proposes a rigorous derivation of the Boltzmann equation in the half-space. We show an analog of the Lanford's theorem in this domain, with specular reflection…