Finite Difference Equations for Transport Effects in Kinetic Theory

Schaeffer该奖项支持对模拟等离子体行为的非线性偏微分方程组的研究。特别考虑了相空间离子密度满足朗道-福克-普朗克方程的等离子体动力学模型。一个主要的焦点是发展有限差分格式，正确地跟踪传输效应。在忽略碰撞的情况下，粒子法被广泛使用，但碰撞算子的计算可以在规则网格上更容易地进行。因此我们对有限差分法很感兴趣。这里的目标是研究实现这些方法的结果和收敛分析（如可行）。这项工作的出发点是解决方案具有球对称性的背景。另一个有趣的问题是弗拉索夫-爱因斯坦系统，其中物质的相对论性运动与爱因斯坦场方程耦合。

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.