# Kinetic multi-component gas system models

Bergman Distinguished Visitor

The lecture will focus on the mathematics of particle systems for mixtures of monoatomic gases with different masses, derived from an statistical flows framework known as kinetic theory of gases.

Single component elastic gas models were introduced by L. Boltzmann and J.C. Maxwell in the last quarter of the nineteenth century giving rise to the mathematical physics theory of thermodynamics by means of statistical mechanics.

Nowadays, the Boltzmann model for the irreversible evolution of probability distribution densities has become a benchmark that can handle random particle interactions modeled by nonlocal multilinear forms modeling ‘mixing’ of their states.

The collision or interaction law, as much as the modeling of the transition probability rates modeled by a quantification of differential cross section for pairwise interactions are crucial components in the dynamics.

We will present some recent rigorous properties developed for the multi-component gas system described by coupled Boltzmann equations corresponding to the dynamics of elastic mixing of particles characterized by their identical shapes (spheres) but different masses.

Irene Martínez Gamba is an Argentine–American mathematician. She works as a Professor of Mathematics at the University of Texas at Austin, where she holds the W.A. Tex Moncreif, Jr. Chair in Computational Engineering and Sciences and is head of the Applied Mathematics Group in the Institute for Computational Engineering and Sciences.

You can learn more about Irene Martínez Gamba at http://www.ma.utexas.edu/users/gamba/