Systems of Conservation Laws - Two-Dimensional Riemann Problems (Hardcover, 2001 ed.)

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.

General

Imprint:	Birkhauser Boston
Country of origin:	United States
Series:	Progress in Nonlinear Differential Equations and Their Applications, 38
Release date:	June 2001
First published:	2001
Authors:	Yuxi Zheng
Dimensions:	235 x 155 x 20mm (L x W x T)
Format:	Hardcover
Pages:	320
Edition:	2001 ed.
ISBN-13:	978-0-8176-4080-4
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematics for scientists & engineers
LSN:	0-8176-4080-0
Barcode:	9780817640804

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