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- DescriptionThis work is based on the lecture tes 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 kwledge 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 nlinearsystems, Glimm's scheme, and large-time asymp- toties.
- Author(s)Yuxi Zheng
- PublisherSpringer-Verlag New York Inc.
- Date of Publication23/10/2012
- Series TitleProgress in Nonlinear Differential Equations and Their Applications
- Series Part/Volume Number36
- Place of PublicationNew York
- Country of PublicationUnited States
- ImprintSpringer-Verlag New York Inc.
- Content Notebiography
- Weight522 g
- Width155 mm
- Height235 mm
- Spine18 mm
- Edition StatementSoftcover reprint of the original 1st ed. 2001
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