Global Propagation of Regular Nonlinear Hyperbolic Waves [electronic resource] / by Li Tatsien, Wang Libin.
Contributor(s): Libin, Wang [author.] | SpringerLink (Online service)Material type: TextSeries: Progress in Nonlinear Differential Equations and Their Applications: 76Publisher: Boston : Birkhäuser Boston, 2009Edition: 1stDescription: X, 252 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780817646356Subject(s): Physics | Mathematical analysis | Analysis (Mathematics) | Differential equations | Partial differential equations | Applied mathematics | Engineering mathematics | Elementary particles (Physics) | Quantum field theory | Physics | Elementary Particles, Quantum Field Theory | Analysis | Theoretical, Mathematical and Computational Physics | Partial Differential Equations | Ordinary Differential Equations | Applications of MathematicsAdditional physical formats: Printed edition:: No titleDDC classification: 539.72 LOC classification: QC793-793.5QC174.45-174.52Online resources: Click here to access online
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Preliminaries -- The Cauchy Problem -- The Cauchy Problem (Continued) -- Cauchy Problem on a Semibounded 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.
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.