Linear and Non-Linear Waves

[9322146]斯特劳斯稳定性和不稳定性现象将在带电粒子有碰撞和无碰撞的动力学理论中进行研究。本文还将研究闵可夫斯基空间中的谐波映射，以及标量场随时间变化的基态的稳定性理论，包括边界的影响。线性和非线性色散波的平滑现象是进一步研究的热点。用于计算机芯片的先进半导体器件是由其特性来源于负电子和正“空穴”运动的材料制成的。这种运动形成一种非线性波动，可以用某些数学方程来描述。我们研究这些运动如何变化，以及它们如何对初始变化敏感。同样的方程描述了科学和工程中的许多其他波动现象，例如能源研究和空间研究。在各种情况下研究了非线性波的灵敏度。目的是确定波浪不稳定行为的根本原因。沃尔特•施特劳斯

9322146 Strauss Stability and instability phenomena will be investigated in the kinetic theory of charged particles both with and without collisions. Also to be studied are harmonic maps in Minkowski space, and the stability theory of time- dependent ground states of scalar fields, including the effects of boundaries. A further focus of research is the smoothing phenomenon for linear and nonlinear dispersive waves.Advanced semiconductor devices, used for computer chips, are made of materials whose properties derive from the movements of negative electrons and positive "holes". Such movements form a type of nonlinear wave and are described by certain mathematical equations. We study how these movements change and how they are sensitive to initial variations. The same kinds of equations describe many other wave phenomena in science and engineering, such as in energy research and space research. The sensitivity of nonlinear waves is studied in a variety of contexts. The purpose is to determine the fundamental reasons for the unstable behavior of waves.Walter Strauss