Front Tracking for Hyperbolic Conservation Laws
Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a self-contained presentation using front tracking, which is also a numerical method. The multidimensional scalar case and the case of systems on the...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2002, 2002
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| Edition: | 1st ed. 2002 |
| Series: | Applied Mathematical Sciences
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Introduction
- 1.1 Notes
- 2 Scalar Conservation Laws
- 2.1 Entropy Conditions
- 2.2 The Riemann Problem
- 2.3 Front Tracking
- 2.4 Existence and Uniqueness
- 2.5 Notes
- 3 A Short Course in Difference Methods
- 3.1 ConservativeMethods
- 3.2 Error Estimates
- 3.3 APriori Error Estimates
- 3.4 Measure-Valued Solutions
- 3.5 Notes
- 4 Multidimensional Scalar Conservation Laws
- 4.1 Dimensional SplittingMethods
- 4.2 Dimensional Splitting and Front Tracking
- 4.3 Convergence Rates
- 4.4 Operator Splitting: Diffusion
- 4.5 Operator Splitting: Source
- 4.6 Notes
- 5 The Riemann Problem for Systems
- 5.1 Hyperbolicity and Some Examples
- 5.2 Rarefaction Waves
- 5.3 The Hugoniot Locus: The Shock Curves
- 5.4 The Entropy Condition
- 5.5 The Solution of the Riemann Problem
- 5.6 Notes
- 6 Existence of Solutions of the Cauchy Problem
- 6.1 Front Tracking for Systems
- 6.2 Convergence
- 6.3 Notes
- 7 Well-Posedness of the Cauchy Problem
- 7.1 Stability
- 7.2 Uniqueness
- 7.3 Notes
- A Total Variation, Compactness, etc.
- A.1 Notes
- B The Method of Vanishing Viscosity
- B.1 Notes
- C Answers and Hints
- References