Jean-Francois Collet

On some models in the kinetic theory of chemical reactions and phase transitions

Abstract :

We will present a certain number of models which describe the chemical
interaction of a population of clusters, in which the main variables are
of chemical nature (e.g. mass, concentration, chemical potential).
These models can be thought of as a microscopic basis for the well-known
equations of chemical kinetics, much in the way classical (Boltzmann)
kinetic theory, which focuses on mechanical variables, provides a
microscopical basis for deriving macroscopic fluid-mechanical equations.

After presenting the (by now) most classical models, we will try to give
a bird's eye-view of what can be said about their large-time behaviour,
while emphasizing the similarity with mechanical kinetic theory. The central
mathematical tool in this context is the use of entropy-like quantities,
some of which have interesting physical interpretations.