Systems of Conservation Laws: Two-Dimensional Riemann Problems / Edition 1

by Yuxi Zheng

Overview

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 2-D 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.

Product Details

ISBN-13:	9780817640804
Publisher:	Birkhäuser Boston
Publication date:	06/29/2001
Series:	Progress in Nonlinear Differential Equations and Their Applications , #38
Edition description:	2001
Pages:	320
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

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.