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Systems of Conservation Laws: Two-Dimensional Riemann Problems (Progress in Nonlinear Differential Equations and Their Applications)

Yuxi Zheng

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ISBN 10: 1461266319 / ISBN 13: 9781461266310
Published by Birkhäuser, 2012
Used Condition: Good Soft cover
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Title: Systems of Conservation Laws: ...

Publisher: Birkhäuser

Publication Date: 2012

Binding: Paperback

Book Condition: Good

About this title


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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