Related papers: Inelastic Boltzmann Equation Driven by a Particle …
The Boltzmann equation for inelastic Maxwell models is used to determine the Navier-Stokes transport coefficients of a granular binary mixture in $d$ dimensions. The Chapman-Enskog method is applied to solve the Boltzmann equation for…
In this paper we consider the stochastic dynamics of a finite system of particles in a finite volume (Kac-like particle system) which annihilate with probability $\alpha \in (0,1)$ or collide elastically with probability $1-\alpha$. We…
This paper deals with the long time behavior of solutions to the spatially homogeneous Boltzmann equation. The interactions considered are the so-called (non cut-off and non mollified) hard potentials. We prove an exponential in time…
We start with some global Maxwellian function $M$, which is a stationary solution (with the constant total density $\rho$) of the Boltzmann equation, and we denote the number of the corresponding space variables by $n$. The notion of…
The diffusion of tracer particles immersed in a granular gas under uniform shear flow (USF) is analyzed within the framework of the inelastic Boltzmann equation. Two different but complementary approaches are followed to achieve exact…
We investigate the large time behavior of solutions to the spatially homogeneous linear Boltzmann equation from a semigroup viewpoint. Our analysis is performed in some (weighted) $L^{1}$-spaces. We deal with both the cases of hard and soft…
We consider the one-dimensional motion of a particle randomly accelerated by Gaussian white noise on the line segment 0<x<1. The reflections of the particle from the boundaries at x=0 and 1 are inelastic, with coefficient of restitution r.…
The paper deals with the homogenization of a linear Boltzmann equation by the means of the sigma-convergence method. Under a general deterministic assumption on the coefficients of the equation, we prove that the density of the particles…
The Boltzmann kinetic equation is considered to evaluate the first-order contributions $T_i^{(1)}$ to the partial temperatures in binary granular suspensions at low density. The influence of the surrounding gas on the solid particles is…
We show the propagation of regularity, uniformly in time, for the scaled solutions of the inelastic Maxwell model for small inelasticity. This result together with the weak convergence towards the homogenous cooling state present in the…
We study the single particle velocity distribution for a granular fluid of inelastic hard spheres or disks, using the Enskog-Boltzmann equation, both for the homogeneous cooling of a freely evolving system and for the stationary state of a…
The Boltzmann H-theorem implies that the solution to the Boltzmann equation tends to an equilibrium, that is, a Maxwellian when time tends to infinity. This has been proved in varies settings when the initial energy is finite. However, when…
The problem of energy conservation in the lattice Boltzmann method is solved. A novel model with energy conservation is derived from Boltzmann's kinetic theory. It is demonstrated that the full thermo-hydrodynamics pertinent to the…
The Boltzmann equation is a fundamental equation in kinetic theory that describes the motion of rarefied gases. In this study, we examine the Boltzmann equation within a $C^1$ bounded domain, subject to a large external potential $\Phi(x)$…
For the spatially homogeneous Boltzmann equation with hard po- tentials and Grad's cutoff (e.g. hard spheres), we give quantitative estimates of exponential convergence to equilibrium, and we show that the rate of exponential decay is…
We compare the steady state velocity distributions from our three-dimensional inelastic hard sphere molecular dynamics simulation for homogeneously heated granular media, with the predictions of a mean field-type Enskog-Boltzmann equation…
Combining analytical and numerical methods, we study within the framework of the homogeneous non-linear Boltzmann equation, a broad class of models relevant for the dynamics of dissipative fluids, including granular gases. We use the new…
Mass transport of a driven granular binary mixture is analyzed from the inelastic Boltzmann kinetic equation for inelastic Maxwell models (IMM). The mixture is driven by a thermostat constituted by two terms: a stochastic force and a drag…
The goal of this work is to present an approach to the homogeneous Boltzmann equation for Maxwellian molecules with a physical collision kernel which allows us to construct unique solutions to the initial value problem in a space of…
In this paper, we prove global in time existence, uniqueness and stability of mild solutions near vacuum for the 4-wave inhomogeneous kinetic wave equation, for Laplacian dispersion relation in dimension $d=2,3$. We also show that for…