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Global Propagation of Regular Nonlinear Hyperbolic Waves

  • Authors
  • Li Tatsien
  • Wang Libin

Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 76)

Table of contents

  1. Front Matter
    Pages i-x
  2. Li Tatsien, Wang Libin
    Pages 1-27
  3. Li Tatsien, Wang Libin
    Pages 29-49
  4. Li Tatsien, Wang Libin
    Pages 51-77
  5. Li Tatsien, Wang Libin
    Pages 79-114
  6. Li Tatsien, Wang Libin
    Pages 115-125
  7. Li Tatsien, Wang Libin
    Pages 127-148
  8. Li Tatsien, Wang Libin
    Pages 149-174
  9. Li Tatsien, Wang Libin
    Pages 175-190
  10. Li Tatsien, Wang Libin
    Pages 191-207
  11. Li Tatsien, Wang Libin
    Pages 209-243
  12. Back Matter
    Pages 1-7

About this book

Introduction

This monograph describes global propagation of regular nonlinear hyperbolic waves described by first-order quasilinear hyperbolic systems in one dimension. The exposition is clear, concise, and unfolds systematically, beginning with introductory material which leads to the original research of the authors.

Using the concept of weak linear degeneracy and the method of (generalized) normalized coordinates, this book establishes a systematic theory for the global existence and blowup mechanism of regular nonlinear hyperbolic waves with small amplitude for the Cauchy problem, the Cauchy problem on a semi-bounded initial data, the one-sided mixed initial-boundary value problem, the generalized Riemann problem, the generalized nonlinear initial-boun dary Riemann problem, and some related inverse problems. Motivation is given via a number of physical examples from the areas of elastic materials, one-dimensional gas dynamics, and waves.

Global Propagation of Regular Nonlinear Hyperbolic Waves will stimulate further research and help readers further understand important aspects and recent progress of regular nonlinear hyperbolic waves.

Keywords

Boundary value problem ODEs PDEs cauchy problem global propagation linear optimization mechanics nonlinear hyperbolic waves nonlinear waves

Bibliographic information

  • DOI https://doi.org/10.1007/b78335
  • Copyright Information Birkhäuser Boston 2009
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4244-0
  • Online ISBN 978-0-8176-4635-6
  • Series Print ISSN 1421-1750
  • Series Online ISSN 2374-0280
  • Buy this book on publisher's site