Global Propagation of Regular Nonlinear Hyperbolic Waves [Hardcover]

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 and leading to the original research of the authors. Topics are motivated with a number of physical examples from the areas of elastic materials, one-dimensional gas dynamics, and waves. Aimed at researchers and graduate students in partial differential equations and related topics, this book will stimulate further research and help readers further understand important aspects and recent progress of regular nonlinear hyperbolic waves.

This monograph describes global propagation of regular nonlinear hyperbolic waves described by first-order quasilinear hyperbolic systems in one dimension. The exposition is clear and concise, unfolds systematically and includes the authors own research.

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

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 initiall3*