Systems of Conservation Laws: Two-Dimensional Riemann Problems: 38 (Progress in Nonlinear Differential Equations and Their Applications) - Hardcover

Zheng, Yuxi

Hardcover

ISBN 10: 0817640800 ISBN 13: 9780817640804

Verlag: Birkhäuser, 2001

Inhaltsangabe

Book by Zheng Yuxi

Über diesen Titel

Reseña del editor:

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.

Reseña del editor:

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 a knowledge of the elementary theory of partial differential equations.

Key features of this work include:

* broad range of topics, from the classical treatment to recent results, dealing with solutions to 2D compressible Euler equations

* good review of basic concepts (1-D Riemann problems)

* concrete solutions presented, with many examples, over 100 illustrations, open problems, and numerical schemes

* numerous exercises, comprehensive bibliography and index

* appeal to a wide audience of applied mathematicians, graduate students, physicists, and engineers Written in a clear, accessible style, the book emphasizes more recent results that will prepare readers to meet modern challenges in the subject, that is, to carry out theoretical, numerical, and asymptotical analysis.

Über diese Auflage

• Verlag: Birkhäuser
• Erscheinungsdatum: 2001
• ISBN 10: 0817640800
• ISBN 13: 9780817640804
• Einband: Tapa dura
• Anzahl der Seiten: 344