In this article we cast the unique solvability of a class of nonautonomous kinetic equations in terms of evolution systems, generalizing semigroup results pertaining to the corresponding autonomous kinetic equations. AMS Subject Classification: 47N55, 82C70

• Kinetic theory studies the macroscopic properties of large numbers of particles, start­ ing from their (classical) equations of motion. Thermodynamics describes the equilibrium behavior of macroscopic objects in terms of concepts such as work, heat, and entropy. The phenomenological laws of thermody­ namics tell us how these quantities are constrained as a system approaches its equilibrium. A...

Everything that is not prohibited is permissible. So, what is prohibited in the course of chemical reactions, heat transfer and other dissipative processes? Is it possible to “overshoot” the equilibrium, and if yes, then how far? Thermodynamically allowed and prohibited trajectories of processes are discussed by the example of effects of equilibrium encircling. The complete theory of thermodyna...

We describe traffic flows in one lane roadways using kinetic theory, with special emphasis on the role of quenched randomness in the velocity distributions. When passing is forbidden, growing clusters are formed behind slow cars and the cluster velocity distribution is governed by an exact Boltzmann equation which is linear and has an infinite memory. The distributions of the cluster size and t...

The paper is concerned with some aspects of stochastic modelling in kinetic theory. First, an overview of the role of particle models with random interactions is given. These models are important both in the context of foundations of kinetic theory and for the design of numerical algorithms in various engineering applications. Then, the class of jump processes with a finite number of states is ...

Recently, an increasing interest in astrophysical as well as laboratory plasmas has been manifested in reference to the existence of relativistic flows, related in turn to the production of intense electric fields in magnetized systems [1]. Such phenomena require their description in the framework of a consistent relativistic kinetic theory, rather than on relativistic MHD equations, subject to...

Approximation theory in the context of probability density function turns out to go beyond the classical idea of orthogonal projection. Special tools have to be designed so as to respect the nonnegativity of the approximate function. We develop here and justify from the theoretical point of view an approximation procedure introduced by Levermore [Levermore, J. Stat. Phys. 83 (1996) 1021–1065] a...