Hyperbolic And Viscous Conservation Laws
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Hyperbolic And Viscous Conservation Laws
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Author : Tai-Ping Liu
language : en
Publisher: SIAM
Release Date : 2000-01-01
Hyperbolic And Viscous Conservation Laws written by Tai-Ping Liu and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Mathematics categories.
An in-depth analysis of wave interactions for general systems of hyperbolic and viscous conservation laws.
Hyperbolic Systems Of Conservation Laws
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Author : Philippe G. LeFloch
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-07-01
Hyperbolic Systems Of Conservation Laws written by Philippe G. LeFloch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-01 with Mathematics categories.
This book examines the well-posedness theory for nonlinear hyperbolic systems of conservation laws, recently completed by the author together with his collaborators. It covers the existence, uniqueness, and continuous dependence of classical entropy solutions. It also introduces the reader to the developing theory of nonclassical (undercompressive) entropy solutions. The systems of partial differential equations under consideration arise in many areas of continuum physics.
Numerical Methods For Conservation Laws
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Author : Randall J. LeVeque
language : en
Publisher: Springer
Release Date : 2012-12-06
Numerical Methods For Conservation Laws written by Randall J. LeVeque and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in de veloping, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable un derstanding of the mathematical structure of these equations and their solutions is first required, and Part I of these notes deals with this theory. Part II deals more directly with numerical methods, again with the emphasis on general tools that are of broad use. I have stressed the underlying ideas used in various classes of methods rather than present ing the most sophisticated methods in great detail. My aim was to provide a sufficient background that students could then approach the current research literature with the necessary tools and understanding. Without the wonders of TeX and LaTeX, these notes would never have been put together. The professional-looking results perhaps obscure the fact that these are indeed lecture notes. Some sections have been reworked several times by now, but others are still preliminary. I can only hope that the errors are. not too blatant. Moreover, the breadth and depth of coverage was limited by the length of these courses, and some parts are rather sketchy.
Systems Of Conservation Laws 1
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Author : Denis Serre
language : en
Publisher: Cambridge University Press
Release Date : 1999-05-27
Systems Of Conservation Laws 1 written by Denis Serre and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-05-27 with Mathematics categories.
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.
Hyperbolic Conservation Laws And The Compensated Compactness Method
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Author : Yunguang Lu
language : en
Publisher: CRC Press
Release Date : 2002-09-27
Hyperbolic Conservation Laws And The Compensated Compactness Method written by Yunguang Lu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-27 with Mathematics categories.
The method of compensated compactness as a technique for studying hyperbolic conservation laws is of fundamental importance in many branches of applied mathematics. Until now, however, most accounts of this method have been confined to research papers. Offering the first comprehensive treatment, Hyperbolic Conservation Laws and the Compensated Comp
Nonlinear Stability Of Shock Waves For Viscous Conservation Laws
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Author : Tai-Ping Liu
language : en
Publisher: American Mathematical Soc.
Release Date : 1985
Nonlinear Stability Of Shock Waves For Viscous Conservation Laws written by Tai-Ping Liu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
In this paper we establish the nonlinear stability of shock waves for viscous conservation laws. It is shown that when the initial data is a perturbation of viscous shock waves, then the solution converges to viscous shock waves, properly translated, as time tends to infinity.
Front Tracking For Hyperbolic Conservation Laws
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Author : Helge Holden
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-08
Front Tracking For Hyperbolic Conservation Laws written by Helge Holden and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-08 with Mathematics categories.
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: "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.
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Author : C. M. Dafermos
language : en
Publisher: 清华大学出版社有限公司
Release Date : 2005
written by C. M. Dafermos and has been published by 清华大学出版社有限公司 this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Conservation laws (Physics) categories.
Viscous Profiles And Numerical Methods For Shock Waves
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Author : Michael Shearer
language : en
Publisher: SIAM
Release Date : 1991-01-01
Viscous Profiles And Numerical Methods For Shock Waves written by Michael Shearer and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-01 with Science categories.
One strongly represented theme is the power of ideas from dynamical systems that are being adapted and developed in the context of shock waves.
Some Current Topics On Nonlinear Conservation Laws
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Author : Ling Hsiao
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Some Current Topics On Nonlinear Conservation Laws written by Ling Hsiao and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This volume resulted from a year-long program at the Morningside Center of Mathematics at the Academia Sinica in Beijing. It presents an overview of nonlinear conversation laws and introduces developments in this expanding field. Zhouping Xin's introductory overview of the subject is followed by lecture notes of leading experts who have made fundamental contributions to this field of research. A. Bressan's theory of $-well-posedness for entropy weak solutions to systems of nonlinear hyperbolic conversation laws in the class of viscosity solutions is one of the most important results in the past two decades; G. Chen discusses weak convergence methods and various applications to many problems; P. Degond details mathematical modelling of semi-conductor devices; B. Perthame describes the theory of asymptotic equivalence between conservation laws and singular kinetic equations; Z. Xin outlines the recent development of the vanishing viscosity problem and nonlinear stability of elementary wave-a major focus of research in the last decade; and the volume concludes with Y. Zheng's lecture on incompressible fluid dynamics. This collection of lectures represents previously unpublished expository and research results of experts in nonlinear conservation laws and is an excellent reference for researchers and advanced graduate students in the areas of nonlinear partial differential equations and nonlinear analysis. Titles in this series are co-published with International Press, Cambridge, MA.