Nonlinear approximation theory for kinetic equations
Location: Hill 705
Date & time: Friday, 29 January 2016 at 4:00PM - 4:11PM
Minh Bin Tran, University of Wisconsin: A challenging problem in solving the Boltzmann equation numerically is that the velocity space is approximated by a finite region and most numerical methods are based on a truncation technique. Moreover, sometimes, non-physical conditions have to be imposed on the equation in order to keep the velocity domain bounded. In this talk, we introduce a nonlinear wavelet approximation for the Boltzmann equation. Our nonlinear approximation is non-truncated and based on a nonlinear, adaptive spectral method associated with a new wavelet filtering technique and a new formulation of the equation. The approximation is proved to converge and preserve most of the properties of the homogeneous Boltzmann equation. It could also be considered as a general frame work for approximating kinetic integral equations.