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Nonlinear Wave Equations
Walter A. Strauss, Brown University, Providence, RI
A co-publication of the AMS and CBMS.
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CBMS Regional Conference Series in Mathematics
1989; 91 pp; softcover
Number: 73
Reprint/Revision History:
reprinted with corrections 1993; fourth printing 1997; fifth printing 2011
ISBN-10: 0-8218-0725-0
ISBN-13: 978-0-8218-0725-5
List Price: US$23
Member Price: US$18.40
All Individuals: US$18.40
Order Code: CBMS/73
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The theory of nonlinear wave equations in the absence of shocks began in the 1960s. Despite a great deal of recent activity in this area, some major issues remain unsolved, such as sharp conditions for the global existence of solutions with arbitrary initial data, and the global phase portrait in the presence of periodic solutions and traveling waves.

This book, based on lectures presented by the author at George Mason University in January 1989, seeks to present the sharpest results to date in this area. The author surveys the fundamental qualitative properties of the solutions of nonlinear wave equations in the absence of boundaries and shocks. These properties include the existence and regularity of global solutions, strong and weak singularities, asymptotic properties, scattering theory and stability of solitary waves. Wave equations of hyperbolic, Schrödinger, and KdV type are discussed, as well as the Yang-Mills and the Vlasov-Maxwell equations.

The book offers readers a broad overview of the field and an understanding of the most recent developments, as well as the status of some important unsolved problems. Intended for mathematicians and physicists interested in nonlinear waves, this book would be suitable as the basis for an advanced graduate-level course.

Reviews

"A valuable collection of the sharpest results known to date on several closely interrelated topics from the theory of nonlinear wave equations ... Although the theory described here is still far from its final form, the reader who studies the book carefully will be rewarded with glimpses of what the final form will some day be ..."

-- Mathematical Reviews

Table of Contents

  • Introduction
  • Invariance
  • Existence
  • Singularities
  • Solutions of small amplitude
  • Scattering
  • Stability of solitary waves
  • Yang-Mills equations
  • Vlasov-Maxwell equations
  • References
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