Abstract:
Kinetic equation is known to converge to fluid in some certain regimes, but the coupling of the two systems when both regimes coexist is still open. The key is to understand the half-space problem that resembles the boundary layer connecting them. In this talk, I will present a unified proof for the well-posedness of a class of linear half-space equations with general incoming data, and propose a Galerkin method to numerically solve it in a systematic way. The main strategy is to use damping-recovering process for coercivity of the collision term, and the even-odd decomposition for resolving the singularity. Numerical results will be shown to demonstrate the accuracy of the algorithm. |