In this paper we study the diffusion approximation to a transport equation that describes the
motion of individuals whose velocity changes are governed by a Poisson process. We show …

Boundaries occur naturally in kinetic equations, and boundary effects are crucial for
dynamics of dilute gases governed by the Boltzmann equation. We develop a mathematical …

Perturbations of Positive Semigroups with Applications is a self-contained introduction to
semigroup theory with emphasis on positive semigroups on Banach lattices and …

Our interest in the study and computation of electromagnetic fields started during the 1990s.
For Franck Assous, it originated from the need to compute precisely the motion of charged …

Abstract One considers the Vlasov-Stokes equations to model the motion of a solid particles
suspension in a Stokes flow. The dispersed phase, is modelled by a transport kinetic …

We are interested in coupled microscopic/macroscopic models describing the evolution of
particles dispersed in a fluid. The system consists in a Vlasov–Fokker–Planck equation to …

This note is devoted to the review of the major results obtained in these ten years on the
existence problem for the Boltzmann equation. The topics cover the local and global …

Interaction with the environment and motion in space are two fundamental features of living
organisms. Also non-living particles like molecules react and move-driven by diffusion. In …

A.–We prove global stability results of DiPerna-Lions renormalized solutions for
the initial boundary value problem associated to some kinetic equations, from which …

Singularities will generally be created at the boundary for the coupled Vlasov-Poisson or
Vlasov-Maxwell systems. However, global classical solutions are constructed for the Vlasov …