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" Systems of Conservation Laws "
by Yuxi Zheng.
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BL
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573421
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b402640
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| Main Entry
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Zheng, Yuxi.
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| Title & Author
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Systems of Conservation Laws : Two-Dimensional Riemann Problems /\ by Yuxi Zheng.
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| Publication Statement
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Boston, MA :: Birkhäuser Boston :: Imprint: Birkhäuser,, 2001.
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| Series Statement
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Progress in Nonlinear Differential Equations and Their Applications ;; 38
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| ISBN
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9781461201410
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: 9781461266310
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| Contents
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1 Problems -- 1.0 Outline -- 1.1 Some models -- 1.2 Basic problems -- 1.3 Some solutions -- 1.4 von Neumann paradoxes -- 1.5 End notes -- I Basics in One Dimension -- 2 One-dimensional Scalar Equations -- 3 Riemann Problems -- 4 Cauchy Problems -- II Two Dimensional Theory -- 5 A 2-D Scalar Riemann Problem -- 6 The 2-D Riemann problem and Pseudo-Characteristics -- 7 Axisymmetric and Self-similar Solutions -- 8 Plausible Structures for 2-D Euler Systems -- 9 The Pressure-Gradient Equations of the Euler Systems -- 10 The Convective Systems of the Euler Systems -- 11 The Two-dimensional Burgers Equations -- III Numerical schemes -- 12 Numerical Approaches -- List of Symbols.
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| Abstract
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This work is based on the lecture notes of the course M742: Topics in Partial Dif ferential Equations, which I taught in the Spring semester of 1997 at Indiana Univer sity. My main intention in this course was to give a concise introduction to solving two-dimensional compressibleEuler equations with Riemann data, which are special Cauchy data. This book covers new theoretical developments in the field over the past decade or so. Necessary knowledge of one-dimensional Riemann problems is reviewed and some popularnumerical schemes are presented. Multi-dimensional conservation laws are more physical and the time has come to study them. The theory onbasicone-dimensional conservation laws isfairly complete providing solid foundation for multi-dimensional problems. The rich theory on ellip tic and parabolic partial differential equations has great potential in applications to multi-dimensional conservation laws. And faster computers make itpossible to reveal numerically more details for theoretical pursuitin multi-dimensional problems. Overview and highlights Chapter 1is an overview ofthe issues that concern us inthisbook. It lists theEulersystemandrelatedmodelssuch as theunsteady transonic small disturbance, pressure-gradient, and pressureless systems. Itdescribes Mach re flection and the von Neumann paradox. In Chapters 2-4, which form Part I of the book, we briefly present the theory of one-dimensional conservation laws, which in cludes solutions to the Riemann problems for the Euler system and general strictly hyperbolic and genuinely nonlinearsystems, Glimm's scheme, and large-time asymp toties.
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Mathematics.
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Global analysis (Mathematics).
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Computer science-- Mathematics.
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SpringerLink (Online service)
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