Related papers: Inelastic Boltzmann Equation Driven by a Particle …
We consider the spatially homogeneous Boltzmann equation for inelastic hard spheres (with constant restitution coefficient $\alpha \in (0,1)$) under the thermalization induced by a host medium with a fixed Maxwellian distribution. We prove…
We consider the spatially homogeneous Boltzmann equation for inelastic hard-spheres (with constant restitution coefficient $\alpha \in (0,1)$) under the thermalization induced by a host medium with a fixed Maxwellian distribution. We prove…
We consider the spatially homogeneous Boltzmann equation for {\em inelastic hard spheres}, in the framework of so-called {\em constant normal restitution coefficients} $\alpha \in [0,1]$. In the physical regime of a small inelasticity (that…
In this paper, we consider the spatially inhomogeneous diffusively driven inelastic Boltzmann equation in different cases: the restitution coefficient can be constant or can depend on the impact velocity (which is a more physically relevant…
We consider a space-homogeneous gas of {\it inelastic hard spheres}, with a {\it diffusive term} representing a random background forcing (in the framework of so-called {\em constant normal restitution coefficients} $\alpha \in [0,1]$ for…
We show the existence of smooth stationary solutions for the inelastic Boltzmann equation under the thermalization induced by a host-medium with a fixed distribution. This is achieved by controlling the Lp-norms, the moments and the…
We study the uniqueness and regularity of the steady states of the diffusively driven Boltzmann equation in the physically relevant case where the restitution coefficient depends on the impact velocity including, in particular, the case of…
We introduce the model of inelastic hard spheres with random restitution coefficient $\alpha$, in order to account for the fact that, in a vertically shaken granular system interacting elastically with the vibrating boundary, the energy…
In this paper, we study the homogeneous inelastic Boltzmann equation for hard spheres. We first prove that the solution $f(t,v)$ is bounded pointwise from above by $C_{f_0}\langle t \rangle^3$ and establish that the cooling time is infinite…
We consider the spatially homogeneous Boltzmann equation for inelastic hard spheres, in the framework of so-called constant normal restitution coefficients. We prove the existence of self-similar solutions, and we give pointwise estimates…
The Boltzmann equation for inelastic and rough hard spheres is considered as a model of a dilute granular gas. In this model, the collisions are characterized by constant coefficients of normal and tangential restitution and hence the…
The Boltzmann equation for d-dimensional inelastic Maxwell models is considered to analyze transport properties in spatially inhomogeneous states close to the simple shear flow. A normal solution is obtained via a Chapman--Enskog--like…
The homogeneous steady state of a fluid of inelastic hard spheres immersed in a bath of elastic hard spheres kept at equilibrium is analyzed by means of the first Sonine approximation to the (spatially homogeneous) Enskog--Boltzmann…
We study the single-particle distributions of three-dimensional hard sphere gas described by the Boltzmann equation. We focus on the steady homogeneous isotropic solutions in thermodynamically open conditions, i.e. in the presence of…
We develop the Cauchy theory of the spatially homogeneous inelastic Boltzmann equation for hard spheres, for a general form of collision rate which includes in particular variable restitution coefficients depending on the kinetic energy and…
We study the Boltzmann equation for a space-homogeneous gas of inelastic hard spheres, with a diffusive term representing a random background forcing. Under the assumption that the initial datum is a nonnegative $L^2$ function, with bounded…
The local balance equations for the density, momentum, and energy of a dilute gas of elastic or inelastic hard spheres, strongly confined between two parallel hard plates are obtained. The starting point is a Boltzmann-like kinetic…
In this paper, we study the spatially homogeneous inelastic Boltzmann equation for the angular cutoff pseudo-Maxwell molecules with an additional term of linear deformation. We establish the existence of non-Maxwellian self-similar profiles…
A univariate polynomial equation is presented. It provides models of the thermal lattice Boltzmann equation. The models can be accurate up to any required level and can be applied to regular lattices, which allow efficient and accurate…
We study the abundance of a particle species in a thermalized plasma by introducing a quantum kinetic description based on the non-equilibrium effective action. A stochastic interpretation of quantum kinetics in terms of a Langevin equation…