Wave Interactions in Continuum Mechanics

University Of Massachusetts Amherst, Amherst MA

Investigators

Abstract

NSF Award Abstract - DMS-0104485 Mathematical Sciences: Wave Interactions in Continuum Mechanics Abstract DMS-0104485 Young, Robin This 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.