제목 : An Introduction to Collisional Kinetic Theory
초록 : In this talk, we will explore several fundamental partial differential equations that arise in collisional kinetic theory. We begin by formally deriving the Boltzmann equation from the N-body dynamics, introducing the BBGKY hierarchy and the Boltzmann-Grad limit. Next, we consider a general collisional kinetic equation for inverse-power law potentials and examine its properties. We will then discuss the grazing collision limit, which leads to the Landau equation—a degenerate nonlinear heat equation. Finally, we establish a connection between the Boltzmann equation for inverse-power law potentials and the hard-sphere Boltzmann equation through the vanishing angular singularity limit.
