Front Tracking for Hyperbolic Conservation Laws: v.152 (Applied Mathematical Sciences) - Hardcover

Holden, Helge; Risebro, N.H.

Hardcover

ISBN 10: 3540432892 ISBN 13: 9783540432890

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 2002

Synopsis

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.

About this title

Review

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)

Synopsis

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 line are treated in detail. A chapter on finite differences is included."It is already one of the few best digests on this topic. The present book is an excellent compromise between theory and practice. Students will appreciate the lively and accurate style." - D. Serre, MathSciNet. "I have read the book with great pleasure, and I can recommend it to experts as well as students. It can also be used for reliable and very exciting basis for a one-semester graduate course." - S. Noelle, Book review, "German Math. Soc". "Making it an ideal first book for the theory of nonlinear partial differential equations...an excellent reference for a graduate course on nonlinear conservation laws." - M. Laforest, "Comp. Phys. Comm".

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 2002
• Language: English
• ISBN 10: 3540432892
• ISBN 13: 9783540432890
• Binding: Hardcover
• Number of pages: 378