Ebook: Systems of Conservation Laws: Two-Dimensional Riemann Problems

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.

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Content:
Front Matter....Pages i-xv
Problems....Pages 1-9
Front Matter....Pages 11-11
One-dimensional Scalar Equations....Pages 13-22
Riemann Problems....Pages 23-47
Cauchy Problems....Pages 49-82
Front Matter....Pages 83-83
A 2-D Scalar Riemann Problem....Pages 85-107
The 2-D Riemann problem and Pseudo-Characteristics....Pages 109-118
Axisymmetric and Self-similar Solutions....Pages 119-193
Plausible Structures for 2-D Euler Systems....Pages 195-210
The Pressure-Gradient Equations of the Euler Systems....Pages 211-226
The Convective Systems of the Euler Systems....Pages 227-233
The Two-dimensional Burgers Equations....Pages 235-261
Front Matter....Pages 263-263
Numerical Approaches....Pages 265-290
Back Matter....Pages 291-320

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Content:
Front Matter....Pages i-xv
Problems....Pages 1-9
Front Matter....Pages 11-11
One-dimensional Scalar Equations....Pages 13-22
Riemann Problems....Pages 23-47
Cauchy Problems....Pages 49-82
Front Matter....Pages 83-83
A 2-D Scalar Riemann Problem....Pages 85-107
The 2-D Riemann problem and Pseudo-Characteristics....Pages 109-118
Axisymmetric and Self-similar Solutions....Pages 119-193
Plausible Structures for 2-D Euler Systems....Pages 195-210
The Pressure-Gradient Equations of the Euler Systems....Pages 211-226
The Convective Systems of the Euler Systems....Pages 227-233
The Two-dimensional Burgers Equations....Pages 235-261
Front Matter....Pages 263-263
Numerical Approaches....Pages 265-290
Back Matter....Pages 291-320
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