ABSTRACT

In asymptotic analysis, kinetic half-space equations are often derived as boundary layer models to bridge kinetic and interior macroscopic equations. These equations arise when one considers kinetic equations for dense gases over bounded domains. Properly captured end-states of the half-space equations are used as the boundary conditions for the interior equations. Therefore it is of great interest to understand the analytical behavior of these equations and to design efficient numerical schemes. In this talk, we will review some recent development in both numerics and analysis related to half-space equations in both one dimension and higher dimensions.