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Birkhäuser - Birkhäuser Physics | Global Propagation of Regular Nonlinear Hyperbolic Waves

Global Propagation of Regular Nonlinear Hyperbolic Waves

Li, Tatsien, Libin, Wang


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  • Provides a complete theory for waves with general system conditions and boundary conditions
  • Features many applications related to mechanics and physics
  • Contains much material based on the results obtained by the authors in recent years

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.

Content Level » Research

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

Related subjects » Birkhäuser Mathematics - Birkhäuser Physics

Table of contents 

Preface.-. Introduction.-. Preliminaries.-.Cauchy problem.-. Cauchy problem (Continued).-. Cauchy Problem on a semi-bounded initial axis.-. One-sided mixed initial-boundary value problem.-.Generalized Riemann problem.-. Generalized nonlinear initial-boundary Riemann problem.-. Inverse generalized Riemann problem.-. Inverse piston problem.-. Bibliography

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