Singularities and Oscillations
By: edited by Jeffrey Rauch, Michael Taylor
Contributors: Taylor, Michael
Series: The IMA Volumes in Mathematics and its Applications -- 91; IMA volumes in mathematics and its applications -- 91.
Publisher: Springer New York
Published: 1997
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 158
ISBN-13: 9781461273622; 9781461219729
Subjects: Mathematics; Global analysis (Mathematics)
Description: The study of singularities and oscillations of waves has progressed along several fronts. A key common feature is the presence of a small scale in the solutions. Recent emphasis has been on nonlinear waves. Nonlinear problems are generally less amenable than linear problems to broad unified approaches. As a result there is a justifiable tendency to concentrate on problems of particular geometric or physical interest. This volume contains a multiplicity of approaches brought to bear on problems varying from the formation of caustics and the propagation of waves at a boundary to the examination of viscous boundary layers. There is an examination of the foundations of the theory of high- frequency electromagnetic waves in a dielectric or semiconducting medium. Unifying themes are not entirely absent from nonlinear analysis. One chapter in the volume considers microlocal analysis, including paradifferential operator calculus, on Morrey spaces, and connections with various classes of partial differential equations.
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Table of contents: title: Foreword; title: Preface; title: Observation and control of elastic waves; title: Modeling the dispersion of light; title: Singularities and oscillations in a nonlinear variational wave equation; title: Viscous boundary layers and high frequency oscillations; title: Nonlinear oscillations and caustics; title: Microlocal analysis on Morrey spaces; title: Nonlinear geometric optics for reflecting and glancing oscillations.