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Quasilinear hyperbolic systems is an important area of partial differential equations with many applications in mechanics, physics and other sciences. In this work a new concept of weak linear degeneracy and normalized coordinates is introduced and its usefulness illustrated in several physical examples. One of the key strengths of the book is the presentation of a complete result for the global existence and blow-up phenomenon of classical solutions to the Cauchy problem for general quasilinear hyperbolic systems with small and decaying initial data. Previous results on this subject obtained by F. John, T.P. Liu and L. Hormander, respectively, may be regarded as special cases. The exposition is clear, concise and unfolds systematically beginning with introductory material. Topics are motivated with a number of physical examples from elastic materials, one-dimensional gas dynamics, motion of an elastic string, and waves. A complete bibliography on the subject and a helpful index are also provided. This book will be of interest to researchers and graduate students in partial differential equations and related topics.

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