
Front Tracking for Hyperbolic Conservation Laws
Springer (Publisher)
1st Edition
Published on 1. July 2002
Book
Hardback
XII, 364 pages
978-3-540-43289-0 (ISBN)
The article will not be published
Description
This book presents the theory of hyperbolic conservation laws from basic theory to the forefront of research.
The text treats the theory of scalar conservation laws in one dimension in detail, showing the stability of the Cauchy problem using front tracking. The extension to multidimensional scalar conservation laws is obtained using dimensional splitting. The book includes detailed discussion of the recent proof of well-posedness of the Cauchy problem for one-dimensional hyperbolic conservation laws, and a chapter on traditional finite difference methods for hyperbolic conservation laws with error estimates and a section on measure valued solutions.
The text treats the theory of scalar conservation laws in one dimension in detail, showing the stability of the Cauchy problem using front tracking. The extension to multidimensional scalar conservation laws is obtained using dimensional splitting. The book includes detailed discussion of the recent proof of well-posedness of the Cauchy problem for one-dimensional hyperbolic conservation laws, and a chapter on traditional finite difference methods for hyperbolic conservation laws with error estimates and a section on measure valued solutions.
Reviews / Votes
From the reviews:MATHEMATICAL REVIEWS".distinguished in the sense that, although its main scope is front tracking.it addresses a larger audience, being also concerned with numerics and applications.The present book is an excellent compromise between theory and practice. Since it contains a lot of theorems, with full proofs, it is a true piece of mathematical analysis. On the other hand, it displays a lot of details and information about numerical approximation for the Cauchy problem. Thus it will be of interest for a wide audience. Students will appreciate the lively and accurate style, the numerous exercises (55 in all) and the fact that the authors systematically avoid side or exotic topics. As mentioned on the back cover, this text is suitable for graduate courses in PDEs and numerical analysis. Since most advanced analytical material is given in appendices, it does not require much background.""The book under review provides a self-contained, thorough, and modern account of the mathematical theory of hyperbolic conservation laws. . gives a detailed treatment of the existence, uniqueness, and stability of solutions to a single conservation law in several space dimensions and to systems in one dimension. This book . is a timely contribution since it summarizes recent and efficient solutions to the question of well-posedness. This book would serve as an excellent reference for a graduate course on nonlinear conservation laws .." (M. Laforest, Computer Physics Communications, Vol. 155, 2003)"The present book is an excellent compromise between theory and practice. Since it contains a lot of theorems, with full proofs, it is a true piece of mathematical analysis. On the other hand, it displays a lot of details and information about numerical approximation for the Cauchy problem. Thus it will be of interest for a wide audience. Students will appreciate the lively and accurate style .. this text is suitable for graduate courses in PDEs and numerical analysis." (Denis Serre, Mathematical Reviews, 2003 e)More details
Series
Edition
1., st ed 2002. Corr. 2nd printing
Language
English
Place of publication
Berlin
Germany
Target group
Professional and scholarly
College/higher education
Research
Edition type
New edition
Product notice
Laminated cover
Illustrations
40
40 s/w Abbildungen
4 black & white illustrations
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Thickness: 22 mm
Weight
712 gr
ISBN-13
978-3-540-43289-0 (9783540432890)
Schweitzer Classification
Other editions
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Helge Holden | Nils Henrik Risebro
Front Tracking for Hyperbolic Conservation Laws
Book
12/2015
2nd Edition
Springer
€106.99
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Additional editions

Helge Holden | Nils H. Risebro
Front Tracking for Hyperbolic Conservation Laws
Book
08/2014
Springer
€53.49
Shipment within 7-9 days

Helge Holden | Nils H. Risebro
Front Tracking for Hyperbolic Conservation Laws
E-Book
11/2013
1st Edition
Springer
€53.49
Available for download
Content
1 Introducation * 2 Scalar Conservation Laws * 3 A Short Course in Difference Methods * 4 Multidimensional Scalar Conservation Laws * 5 The Riemann Problem for Systems * 6 Existence of Solutions of the Cauchy Problem * 7 Wellposedness of the Cauchy Problem * A Total Variation, Compactedness, etc. * B The Method of Vanishing Viscosity * C Answers and Hints * References * Index