Wave Interactions in Continuum Mechanics

美国国家科学基金会奖摘要-DMS-0104485数学科学：连续介质力学中的波相互作用摘要DMS-0104485杨，罗宾这个项目是对非线性双曲波及其相互作用的研究。 波在科学中无处不在，对它们相互作用的一般理解具有根本的兴趣和重要性。 该项目将通过直接和渐近方法系统地开发一个双重框架，用于理解波及其相互作用。 相互作用对波的详细描述，并结合在一个连贯的方式来描述结构的一般解决方案。 这些方法将应用于连续介质力学的几个重要系统。波动的数学理论处于数学和物理的交叉点，并应用于许多工程问题。 这个项目开发的方法来理解一般系统中的波相互作用的结果。 本研究所得结果将可用于弹性固体材料性质的实验测量。

NSF Award Abstract - DMS-0104485Mathematical Sciences: Wave Interactions in Continuum Mechanics AbstractDMS-0104485Young, RobinThis project is a study of nonlinear hyperbolic waves and their interactions. Waves are ubiquitous in science, and a general understanding of their interactions is of fundamental interest and importance. This project will systematically develop a dual framework for understanding waves and their interactions, via direct and asymptotic methods. Interacting pairs of waves are described in detail, and are combined in a coherent fashion to describe the structure of general solutions. These methods will be applied to several important systems of continuum mechanics.The mathematical theory of waves lies at the intersection of mathematics and physics and has application to many engineering problems. This project develops methods for understanding the results of wave interactions in general systems. The results obtained in this study will be of use in experimentally measuring material properties of elastic solids.