9731956 Schaeffer This award supports research on systems of nonlinear partial differential equations which model plasma behavior. In particular a kinetic model of plasma in which the density of ions in phase space satisfies the Landau-Fokker-Planck equation is considered. A major focus is to develop finite difference schemes which correctly track the transport effects. In the case where collisions are neglected, particle methods are widely used, but the computation of the collision operator may be carried out more easily on a regular grid. Hence the interest in a finite difference method. The goals here are to study both the results of implementing such methods and analysis of convergence (as feasible). The starting point for this work is the context in which solutions have spherical symmetry. An additional problem of interest is the Vlasov-Einstein system in which the relativistic motion of matter is coupled to the Einstein field equations.
