Title: Stationary solutions of the Vlasov-Poisson system with diffusive boundary conditions

Abstract: Under certain physical conditions (high temperature, low density) a plasma can be modeled by a system of equations known as the Vlasov-Poisson (VP) system. This system in the case of whole space has been well studied and by now many important issues have been addressed. However, despite its importance in physical applications, the behavior of the particles at a boundary is generally poorly understood. In the first part of the talk we will discuss the basic issues regarding the boundary problem and present some results for the stationary VP system with partially absorbing and diffusively reflecting boundary conditions. The existence and uniqueness will be shown in one and higher dimensions under various settings.