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Overview"This is the second edition of a well-received book providing the fundamentals of the theory hyperbolic conservation laws. Several chapters have been rewritten, new material has been added, in particular, a chapter on space dependent flux functions and the detailed solution of the Riemann problem for the Euler equations. 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. From the reviews of the first edition: ""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." Full Product DetailsAuthor: Helge Holden , Nils Henrik RisebroPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: Softcover reprint of the original 2nd ed. 2015 Volume: 152 Weight: 1.001kg ISBN: 9783662568996ISBN 10: 3662568993 Pages: 517 Publication Date: 21 March 2019 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsPreface.- Introduction.- Scalar Conservation Laws.- A Short Course in Difference Methods.- Multidimensional Scalar Conservation Laws.- The Riemann Problem for Systems.- Existence of Solutions of the Cauchy Problem.- Well-Posedness of the Cauchy Problem.- Conservation Laws with Discontinuous Flux Functions.- Total Variation, Compactness etc.- The Method of Vanishing Viscosity.- Answers and Hints.- Index.ReviewsThis is the 2nd edition of the famous book ... devoted to the modern theory of hyperbolic conservation laws. ... The book is well written, well illustrated (it contains even cartoons) and may be recommended not only to experienced specialists in conservation laws but also to students specialized in this field. (Evgeniy Panov, zbMATH 1346.35004, 2016) “This is the 2nd edition of the famous book … devoted to the modern theory of hyperbolic conservation laws. … The book is well written, well illustrated (it contains even cartoons) and may be recommended not only to experienced specialists in conservation laws but also to students specialized in this field.” (Evgeniy Panov, zbMATH 1346.35004, 2016) Author InformationHelge Holden is professor of mathematics at the Norwegian University of Science and Technology and an adjunct professor at the Center of Mathematics for Applications, part of the University of Oslo. He has done extensive research in stochastic analysis, in particular in its application to flow in porous media. Nils Henrik Risebro is professor of mathematics at the University of Oslo. His research interests are mainly nonlinear partial differential equations and numerical methods for these. He has also worked on conservation laws with discontinuous coefficients in a variety of applications. Tab Content 6Author Website:Countries AvailableAll regions |
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