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Finite Volume Methods for Hyperbolic Problems
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Randall J Leveque, M J Ablowitz (Editor), S H Davis (Editor)
This book contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and ...
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Analysis and Numerics for Conservation Laws
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Gerald Warnecke (Editor)
The priority research program Analysis and Numerics for Conservation Laws was funded by the German research foundation Deutsche Forschungsgemeinschaft (DFG) for a period of six years starting in 1997. The diversity of topics, represented in the present book, was one of the strengths of the research program. Research groups of very different ...
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Front Tracking for Hyperbolic Conservation Laws
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Helge Holden, Nils Henrik Risebro
Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a self-contained presentation using front tracking, which is also a numerical method. The multidimensional scalar case and the case of systems on the line are treated in detail. A chapter on finite ...
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Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables
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Andrew Majda
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Elements of Continuum Mechanics and Conservation Laws
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Sergei K Godunov, Evgenii I Romenskii, S D Mahanti (Editor)
"Elements of Continuum Mechanics and Conservation Laws" presents a systematization of different models in mathematical physics, a study of the structure of conservation laws, thermodynamical identities, and connection with criteria for well-posedness of the corresponding mathematical problems. The theory presented in this book stems from research ...
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Systems of Conservation Laws
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Yuxi Zheng
This work should serve as an introductory text for graduate students and researchers working in the important area of partial differential equations with a focus on problems involving conservation laws. The only requisite for the reader is knowledge of the elementary theory of partial differential equations. Key features of this work include: ...
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Biased Technical Change and Economic Conservation Laws
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Ryuzo Sato
Productivity of inputs is an important determinant of the competitiveness of firms in national and international markets. Productivity growth arises from deliberate decisions to innovate but the technological opportunities could be such that different inputs would have different rates of growth. Previous literature has mostly concentrated on labor ...
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Analysis of Systems of Conservation Laws
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Heinrich Freistuhler (Editor), Freistuhler Freistuhler
Systems of partial differential equations reflecting conservation laws hold significant relevance to a variety of theoretical and practical applications, including compressible fluid flow, electromagnetism, elasticity theory, and other areas of continuum mechanics. This field of nonlinear analysis is currently experiencing a marked increase in ...
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Symmetries of Partial Differential Equations
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A M Vinogradov (Editor)
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Hyperbolic Systems of Conservation Laws: The Theory of Classical and Nonclassical Shock Waves
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Philippe G Lefloch
This is a self-contained exposition of the well-posedness theory for nonlinear hyperbolic systems of conservation laws, completed by the author together with his collaborators. The systems of partial differential equations under consideration arise in many areas of continuum physics. No familiarity with the subject is assumed, so the book can be ...
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Hyperbolic Conservation Laws and the Compensated Compactness Method
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Alan Jeffrey, Lu Yunguang, Yunguang Lu
The method of compensated compactness as a technique for studying hyperbolic conservation laws is of fundamental importance in many branches of applied mathematics. Until now, however, most accounts of this method have been confined to research papers. Offering the first comprehensive treatment, Hyperbolic Conservation Laws and the Compensated ...
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Numerical Methods for Conservation Laws
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by
Randall J Leveque
These notes were developed for a graduate-level course on the theory and numerical solution of nonlinear hyperbolic systems of conservation laws. Part I deals with the basic mathematical theory of the equations: the notion of weak solutions, entropy conditions, and a detailed description of the wave structure of solutions to the Riemann problem. ...
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Systems of Conservation Laws 1: Hyperbolicity, Entropies, Shock Waves
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Denis Serre, I N Sneddon (Translator)
Systems of conservation laws arise naturally in physics and chemistry. To understand them and their consequences (shock waves, finite velocity wave propagation) properly in mathematical terms requires, however, knowledge of a broad range of topics. This book sets up the foundations of the modern theory of conservation laws, describing the physical ...
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Systems of Conservation Laws 2: Geometric Structures, Oscillations, and Initial-Boundary Value Problems
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Denis Serre, I N Sneddon (Translator)
Systems of conservation laws arise naturally in physics and chemistry. Following on from the previous volume, the author considers the maximum principle from the viewpoints of both viscous approximation and numerical schemes. Convergence is studied through compensated compactness. This tool is applied to the description of large amplitude wave ...
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Numerical Approximation of Hyperbolic Systems of Conservation Laws
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by
Edwige Godlewski, Pierre-Arnaud Raviart, Goolewski
This work is devoted to the theory and approximation of nonlinear hyperbolic systems of conservation laws in one or two spaces variables. It follows directly a previous publication on hyperbolic systems of conservation laws by the same authors. While in the earlier publication, the authors concentrate on the mathematical theory of multidimensional ...
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Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves
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Peter D. Lax
This book deals with the mathematical side of the theory of shock waves. The author presents what is known about the existence and uniqueness of generalized solutions of the initial value problem subject to the entropy conditions. The subtle dissipation introduced by the entropy condition is investigated and the slow decay in signal strength it ...
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Numerical Schemes for Conservation Laws
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by
Dietmar Kroner
This book systematically studies upwind methods for initial value problems for scalar conservation laws in one- and multidimensions. The mathematical theory of convergence theory and of a priori error estimates is presented in detail for structure (finite difference methods) as well as for unstructured grids (finite volume methods). Higher order ...
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Hyperbolic Systems of Conservation Laws: The One-Dimensional Cuachy Problem
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Alberto Bressan
This book provides a self-contained introduction to the mathematical theory of hyperbolic systems of conservation laws, with particular emphasis on the study of discontinuous solutions, characterized by the appearance of shock waves. This area has experienced substantial progress in very recent years thanks to the introduction of new techniques, ...
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Symmetries and Recursion Operators for Classical and Supersymmetric Differential Equations
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I S Krasil'shchik, P H M Kersten
This is a detailed exposition of algebraic and geometrical aspects related to the theory of symmetries and recursion operators for nonlinear partial differential equations (PDE), both in classical and in super, or graded, versions. It contains an original theory of Frolicher-Nijenhuis brackets which is the basis for a special cohomological theory ...
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The Riemann Problem for the Transportation Equations in Gas Dynamics
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Wancheng Sheng, Tung Chang, Wang Shengwang
In this volume, the one-dimensional and two-dimensional Riemann problems for the transportation equations in gas dynamics are solved constructively. In either the 1-D or 2-D case, there are only two kinds of solutions: one involves Dirac delta waves, and the other involves vacuums, which have been merely discussed so far. The generalized Rankine ...
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Some Current Topics on Nonlinear Conservation Laws: Lectures at the Morningside Center of Mathematics, 1
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by
Ling Hsiao
This volume resulted from a year-long program at the Morningside Center of Mathematics at the Academia Sinica in Beijing. It presents an overview of nonlinear conversation laws and introduces developments in this expanding field. Xin's introductory overview of the subject is followed by lecture notes of leading experts who have made fundamental ...
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Hyperbolic and Viscous Conservation Laws
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Tai-Ping Liu
Here is an in-depth, up-to-date analysis of wave interactions for general systems of hyperbolic and viscous conservation laws. This self-contained study of shock waves explains the new wave phenomena from both a physical and a mathematical standpoint. The analysis is useful for the study of various physical situations, including nonlinear ...
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Kinetic Formulation of Conservation Laws
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Benoit Perthame
This book gives a general presentation of the mathematical and numerical connections kinetic theory and conservation laws based on several earlier works with P. L. Lions and E. Tadmor, as well as on more recent developments. The kinetic formalism approach allows the reader to consider Partial Differential Equations, such as some nonlinear ...
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An Introduction to Recent Developments in Theory and Numerics for Conservation Laws: Proceedings of the International School on Theory and Numerics for Conservation Laws, Freiburg/Littenweiler, October 20-24, 1997
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by
Dietmar Kroner, Christian Rohde, Mario Ohlberger
The book concerns theoretical and numerical aspects of systems of conservation laws, which can be considered as a mathematical model for the flows of inviscid compressible fluids.Five leading specialists in this area give an overview of the recent results, which include: kinetic methods, non-classical shock waves, viscosity and relaxation methods, ...
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Admissible Solutions of Hyperbolic Conservation Laws
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Tai-Ping Liu
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