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Systems of Conservation Laws Vol. 1  :  Hyperbolicity, Entropies, Shock Waves - Denis Serre

Systems of Conservation Laws Vol. 1

Hyperbolicity, Entropies, Shock Waves

By: Denis Serre, I. N. Sneddon (Translator, Translator)

Hardcover Published: 12th January 2011
ISBN: 9780521582339
Number Of Pages: 286

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Systems of conservation laws arise naturally in physics and chemistry. To understand them and their consequences (shock waves, finite velocity wave propagation) properly in mathematical terms requires, however, knowledge of a broad range of topics. This book sets up the foundations of the modern theory of conservation laws, describing the physical models and mathematical methods, leading to the Glimm scheme. Building on this the author then takes the reader to the current state of knowledge in the subject. The maximum principle is considered from the viewpoint of numerical schemes and also in terms of viscous approximation. Small waves are studied using geometrical optics methods. Finally, the initial-boundary problem is considered in depth. Throughout, the presentation is reasonably self-contained, with large numbers of exercises and full discussion of all the ideas. This will make it ideal as a text for graduate courses in the area of partial differential equations.

Acknowledgments
Introduction
Some modelsp. 1
Scalar equations in dimension d = 1p. 25
Linear and quasi-linear systemsp. 68
Dimension d = 1, the Riemann problemp. 106
The Glimm schemep. 146
Second order perturbationsp. 186
Viscosity profiles for shock wavesp. 220
Bibliographyp. 255
Indexp. 261
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780521582339
ISBN-10: 0521582334
Audience: Professional
Format: Hardcover
Language: English , French
Number Of Pages: 286
Published: 12th January 2011
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 24.7 x 17.4  x 1.7
Weight (kg): 0.59

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