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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.

Differential equations, Hyperbolic. --- Nonlinear wave equations. --- Applied Mathematics --- Engineering & Applied Sciences --- Nonlinear wave equations --- Differential equations, Hyperbolic --- Hyperbolic differential equations --- Physics. --- Mathematical analysis. --- Analysis (Mathematics). --- Differential equations. --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Elementary particles (Physics). --- Quantum field theory. --- Elementary Particles, Quantum Field Theory. --- Analysis. --- Theoretical, Mathematical and Computational Physics. --- Partial Differential Equations. --- Ordinary Differential Equations. --- Applications of Mathematics. --- Wave equation --- Differential equations, Partial --- Quantum theory. --- Global analysis (Mathematics). --- Differential equations, partial. --- Differential Equations. --- Mathematics. --- Math --- Science --- 517.91 Differential equations --- Differential equations --- Partial differential equations --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Mathematical physics. --- 517.1 Mathematical analysis --- Mathematical analysis --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Engineering --- Engineering analysis --- Physical mathematics --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Nuclear physics --- Mathematics

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This two-volume book is devoted to mathematical theory, numerics and applications of hyperbolic problems. Hyperbolic problems have not only a long history but also extremely rich physical background. The development is highly stimulated by their applications to Physics, Biology, and Engineering Sciences; in particular, by the design of effective numerical algorithms. Due to recent rapid development of computers, more and more scientists use hyperbolic partial differential equations and related evolutionary equations as basic tools when proposing new mathematical models of various phenomena and

Differential equations, Hyperbolic --- Differential equations, Nonlinear --- Differential equations, Partial

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The Ginzburg-Landau equation as a mathematical model of superconductors has become an extremely useful tool in many areas of physics where vortices carrying a topological charge appear. The remarkable progress in the mathematical understanding of this equation involves a combined use of mathematical tools from many branches of mathematics. The Ginzburg-Landau model has been an amazing source of new problems and new ideas in analysis, geometry and topology. This collection will meet the urgent needs of the specialists, scholars and graduate students working in this area or related areas.

Singularities (Mathematics) --- Mathematical physics. --- Superconductors --- Superfluidity --- Differential equations, Nonlinear --- Numerical analysis --- Condensed degenerate gases --- Degenerate gases, Condensed --- Superfluids --- Liquid helium --- Low temperatures --- Quantum statistics --- Superconductivity --- Superconducting materials --- Superconductive devices --- Cryoelectronics --- Electronics --- Solid state electronics --- Physical mathematics --- Physics --- Geometry, Algebraic --- Mathematics. --- Numerical solutions. --- Materials --- Mathematics

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Mathematics

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This book collects papers mainly presented at the "International Conference on Partial Differential Equations: Theory, Control and Approximation" (May 28 to June 1, 2012 in Shanghai) in honor of the scientific legacy of the exceptional mathematician Jacques-Louis Lions. The contributors are leading experts from all over the world, including members of the Academies of Sciences in France, the USA and China etc., and their papers cover key fields of research, e.g. partial differential equations, control theory and numerical analysis, that Jacques-Louis Lions created or contributed so much to establishing.

Mathematics. --- Differential equations, Partial. --- Numerical analysis. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Partial differential equations --- Math --- Partial differential equations. --- Calculus of variations. --- Partial Differential Equations. --- Calculus of Variations and Optimal Control; Optimization. --- Numerical Analysis. --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Science --- Differential equations, partial. --- Isoperimetrical problems --- Variations, Calculus of --- Lions, J.-L.