Stephen Pankavich, Department of Applied Mathematics and Statistics, 欧美口爆视频 School of Mines Kinetic Models of Collisionless Plasmas Collisionless plasmas arise in a variety of settings, ranging from magnetically confined plasmas for thermonuclear research to space plasmas in planetary magnetospheres and solar winds. The two fundamental models that describe such phenomena are systems of nonlinear partial differential equations known as the Vlasov-Maxwell (VM) and Vlasov-Poisson (VP) systems. In this talk, we derive these related systems and discuss the possibility of shocks arising from a continuous initial distribution of particles. In the process of this investigation, it will be important to delineate the difference between the mathematical formulation of a shock and the phenomena often described by physicists. Finally, if time remains, we will describe the celebrated phenomenon known as Landau Damping and discuss some recent results.