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- ISBN: 9780817642440 | 0817642447
- Cover: Hardcover
- Copyright: 6/25/2009
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.A systematic theory is established'”by means of the concept of weak linear degeneracy and the method of (generalized) normalized coordinates'”for the global existence and blow-up mechanism of regular nonlinear hyperbolic waves with small amplitude for the Cauchy problem and many others, including the Cauchy problem on a semi-bounded initial data, the one-side mixed initial-boundary value problem, the generalized Riemann problem, and the generalized nonlinear initial-boundary Riemann problem.Topics are motivated with a number of physical examples from the areas of elastic materials, one-dimensional gas dynamics, and waves. This book will stimulate further research and help readers further understand important aspects and recent progress of regular nonlinear hyperbolic waves.