Overview
- Provides a complete theory for waves with general system conditions and boundary conditions
- Features many related applications to mechanics and physics
- Contains much material based on the results obtained by the authors is recent years
Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 76)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Bibliographic Information
Book Title: Global Propagation of Regular Nonlinear Hyperbolic Waves
Authors: Li Tatsien, Wang Libin
Series Title: Progress in Nonlinear Differential Equations and Their Applications
DOI: https://doi.org/10.1007/b78335
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Boston 2009
Hardcover ISBN: 978-0-8176-4244-0Published: 29 June 2009
eBook ISBN: 978-0-8176-4635-6Published: 01 September 2009
Series ISSN: 1421-1750
Series E-ISSN: 2374-0280
Edition Number: 1
Number of Pages: X, 252
Topics: Elementary Particles, Quantum Field Theory, Analysis, Theoretical, Mathematical and Computational Physics, Partial Differential Equations, Ordinary Differential Equations, Applications of Mathematics