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Front Tracking for Hyperbolic Conservation Laws

2015-12-10 Mathematics
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Release : 2015-12-10
Genre : Mathematics
Kind : eBook
Book Rating : 073/5 ( reviews)

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Book Synopsis Front Tracking for Hyperbolic Conservation Laws by : Helge Holden

Download or read book Front Tracking for Hyperbolic Conservation Laws written by Helge Holden. This book was released on 2015-12-10. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Hyperbolic Systems of Conservation Laws

2000 Mathematics
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Release : 2000
Genre : Mathematics
Kind : eBook
Book Rating : 000/5 ( reviews)

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Book Synopsis Hyperbolic Systems of Conservation Laws by : Alberto Bressan

Download or read book Hyperbolic Systems of Conservation Laws written by Alberto Bressan. This book was released on 2000. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to the mathematical theory of hyperbolic systems of conservation laws, with particular emphasis on the study of discontinuous solutions, characterized by the appearance of shock waves. This area has experienced substantial progress in very recent years thanks to the introduction of new techniques, in particular the front tracking algorithm and the semigroup approach. These techniques provide a solution to the long standing open problems of uniqueness and stability of entropy weak solutions. This volume is the first to present a comprehensive account of these new, fundamental advances. It also includes a detailed analysis of the stability and convergence of the front tracking algorithm. A set of problems, with varying difficulty is given at the end of each chapter to verify and expand understanding of the concepts and techniques previously discussed. For researchers, this book will provide an indispensable reference to the state of the art in the field of hyperbolic systems of conservation laws.

Wave Propagation Schemes, Operator Splitting, and Front Tracking for Hyperbolic Conservation Laws

1996 Conservation laws (Mathematics)
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Release : 1996
Genre : Conservation laws (Mathematics)
Kind : eBook
Book Rating : 256/5 ( reviews)

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Book Synopsis Wave Propagation Schemes, Operator Splitting, and Front Tracking for Hyperbolic Conservation Laws by : Universitetet i Oslo. Institute for Informatics

Download or read book Wave Propagation Schemes, Operator Splitting, and Front Tracking for Hyperbolic Conservation Laws written by Universitetet i Oslo. Institute for Informatics. This book was released on 1996. Available in PDF, EPUB and Kindle. Book excerpt:

Analysis of Systems of Conservation Laws

1998-12-30 Mathematics
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Release : 1998-12-30
Genre : Mathematics
Kind : eBook
Book Rating : 440/5 ( reviews)

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Book Synopsis Analysis of Systems of Conservation Laws by : Heinrich Freistuhler

Download or read book Analysis of Systems of Conservation Laws written by Heinrich Freistuhler. This book was released on 1998-12-30. Available in PDF, EPUB and Kindle. Book excerpt: Systems of partial differential equations reflecting conservation laws hold significant relevance to a variety of theoretical and practical applications, including compressible fluid flow, electromagnetism, elasticity theory, and other areas of continuum mechanics. This field of nonlinear analysis is currently experiencing a marked increase in successful research activity. The EU-TMR network "Hyperbolic Systems of Conservation Laws held a summer program offering short courses on the Analysis of Systems of Conservation Laws. This book contains five of the self-contained short courses presented during this program by experts of international reputation. These courses, which address solutions to hyperbolic systems by the front tracking method, non-strictly hyperbolic conservation laws, hyperbolic-elliptic coupled systems, hyperbolic relaxation problems, the stability of nonlinear waves in viscous media and numerics, and more, represent the state of the art of most central aspects of the field.

Hyperbolic Systems of Conservation Laws

2002-07-01 Mathematics
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Release : 2002-07-01
Genre : Mathematics
Kind : eBook
Book Rating : 872/5 ( reviews)

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Book Synopsis Hyperbolic Systems of Conservation Laws by : Philippe G. LeFloch

Download or read book Hyperbolic Systems of Conservation Laws written by Philippe G. LeFloch. This book was released on 2002-07-01. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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