Prmblems In Linear & Nonlinear Wave Motion

特别是在强激光和流体动力学建模中产生的非线性双曲型偏微分方程的全局正则性和短波长渐近展开是该提案的中心主题。这两种方法的一个目标是更好地理解在强烈的超短激光脉冲中观察到的长寿命细丝的聚焦。估计证明规则性或故障的解决方案的推导，以及焦点附近的非线性几何光学展开的研究是关键目标。 目的是研究描述强波传播和相互作用的基本方程的解。这些方程不能精确求解，因此发展了精确的近似方法和严格的定性方法。特别感兴趣的两个问题是强激光与物质的相互作用，以及复杂的流体流动。 一个目标是发展与射线光学的经典思想有关的方法。这些方法在发现和分析新现象方面已经发挥了重要作用。

DMS-9500823 Rauch Global regularity and short wavelength asymptotic expansions of nonlinear hyperbolic partial differential equations arising, in particular, in the modelling of intense lasers and fluid dynamics are the central themes of the proposal. One goal for both methods is to understand better the focussing into long lived filaments that is observed in intense ultra brief laser pulses. The derivations of estimates proving regularity or breakdown of solutions, and, the study of nonlinear geometric optics expansions near focal points are key objectives. The objective is to study the solutions of fundamental equations describing the propagation and interaction of intense waves. These equations cannot be solved exactly so incisive approximate methods together with rigorous qualitative methods are developed. Two problems of particular interest are the interaction of intense lasers with matter, and, complex fluid flows. A goal is to develope methods related to the classical ideas of ray optics. Such methods have already played an important role in the discovery and analysis of new phenomena.