Speaker: Irene M. Gamba
Affiliation: Department of Mathematics and the Institute for Computational Engineering and Sciences (ICES) at The University of Texas – Austin
Title: The Mathematics of statistically interacting flows
Statistical mechanics and kinetic collisional modeling were introduced in the last quarter of the nineteenth century by L. Boltzmann and J.C. Maxwell, independently. These type of evolution models concerns a class of non-local, and nonlinear problems whose rigorous mathematical treatment and approximations are still emerging in comparison to classical non-linear PDE theory. Their applications range from rarefied elastic and inelastic gas dynamics, collisional plasmas and electron transport in nanostructures, to self-organized or social interacting dynamics.
We will see that based on a Markovian framework of birth and death processes under the regime of molecular chaos propagation, their evolution is described by equations of non-linear non-local interacting type called collisional Boltzmann type equations.
We will discuss recent progress in analytical and numerical methods for initial and boundary value problems.
Date: September 7, 2016
Time: 11am -12.00 noon