Related papers: Some exact results for Boltzmann's annihilation dy…
This work is devoted to the analysis of the linear Boltzmann equation in a bounded domain, in the presence of a force deriving from a potential. The collision operator is allowed to be degenerate in the following two senses: (1) the…
The controversial problem of an isolated system with an internal adiabatic wall is investigated with the use of a simple microscopic model and the Boltzmann equation. In the case of two infinite volume one-dimensional ideal fluids separated…
An approximation scheme for model disordered solids is proposed that leads to the fully analytical evaluation of the elastic constants under explicit account of the inhomogeneity (nonaffinity) of the atomic displacements. The theory is in…
We establish pointwise polynomial decay estimates in velocity space for the spatially inhomogeneous Boltzmann equation without cutoff, in the case of hard potentials ($\gamma +2s > 2$), under the assumption that the mass, energy, and…
We study the long-time dynamics of the time-evolutionary Boltzmann equation with hard sphere collisions in the three-dimensional half-space \( \mathbb{R}^2 \times \mathbb{R}^+\), subject to diffuse reflection boundary conditions and small…
In this paper, convergence results on the solutions of a time and space discrete model approximation of the Boltzmann equation for a gas of Maxwellian particles in a bounded domain, obtained by Babovsky and Illner [1989], are extended to…
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…
Studies in the collective motility of organisms use a range of analytical approaches to formulate continuous kinetic models of collective dynamics from rules or equations describing agent interactions. However, the derivation of these…
This is a continuation of our series of works for the inhomogeneous Boltzmann equation. We study qualitative properties of classical solutions, precisely, the full regularization in all variables, uniqueness, non-negativity and convergence…
This paper studies a Boltzmann-Nordheim equation in a slab with two-dimensional velocity space and pseudo-Maxwellian forces. Strong solutions are obtained for the Cauchy problem with large initial data in an $ L^1 \cap L^{\infty} $ setting.…
Within the framework of the homogeneous non-linear Boltzmann equation, we present a new analytic method, without the intrinsic limitations of existing methods, for obtaining asymptotic solutions. This method permits extension of existing…
In coalescing ballistic annihilation, infinitely many particles move with fixed velocities across the real line and, upon colliding, either mutually annihilate or generate a new particle. We compute the critical density in symmetric…
We study freely evolving and forced inelastic gases using the Boltzmann equation. We consider uniform collision rates and obtain analytical results valid for arbitrary spatial dimension d and arbitrary dissipation coefficient epsilon. In…
A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model fluids with excluded volume effects. This is achieved through the use of biased stochastic multi-particle collisions which…
In reaction-diffusion models of annihilation reactions in low dimensions, single-particle dynamics provides a bottleneck for reactions, leading to an anomalously slow approach to the empty state. Here, we construct a reaction model with a…
The article describes Boltzmann equations for a potential case of multi-particle dark matter with symmetric and asymmetric dark matter components in a model-independent approach. We focus on the specific scenario where one of the DM…
Boltzmann equation describes the time development of the velocity distribution in the continuum fluid matter. We formulate the equation using the field theory where the {\it velocity-field} plays the central role. The properties of the…
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…
An alternative equilibrium stochastic dynamics for a Brownian particle in inhomogeneous space is derived. Such a dynamics can model the motion of a complex molecule in its conformation space when in equilibrium with a uniform heat bath. The…
We consider the quantum many-body dynamics at the weak-coupling scaling. We derive rigorously the quantum Boltzmann equation, which contains the classical hard sphere model and, effectively, the inverse power law model, from the many-body…