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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.

Numerical Approximation of Hyperbolic Systems of Conservation Laws

2021-08-28 Mathematics
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Release : 2021-08-28
Genre : Mathematics
Kind : eBook
Book Rating : 448/5 ( reviews)

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Book Synopsis Numerical Approximation of Hyperbolic Systems of Conservation Laws by : Edwige Godlewski

Download or read book Numerical Approximation of Hyperbolic Systems of Conservation Laws written by Edwige Godlewski. This book was released on 2021-08-28. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the theory and approximation by finite volume methods of nonlinear hyperbolic systems of conservation laws in one or two space variables. It follows directly a previous publication on hyperbolic systems of conservation laws by the same authors. Since the earlier work concentrated on the mathematical theory of multidimensional scalar conservation laws, this book will focus on systems and the theoretical aspects which are needed in the applications, such as the solution of the Riemann problem and further insights into more sophisticated problems, with special attention to the system of gas dynamics. This new edition includes more examples such as MHD and shallow water, with an insight on multiphase flows. Additionally, the text includes source terms and well-balanced/asymptotic preserving schemes, introducing relaxation schemes and addressing problems related to resonance and discontinuous fluxes while adding details on the low Mach number situation.

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.

Systems of Conservation Laws 1

1999-05-27 Mathematics
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Release : 1999-05-27
Genre : Mathematics
Kind : eBook
Book Rating : 414/5 ( reviews)

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Book Synopsis Systems of Conservation Laws 1 by : Denis Serre

Download or read book Systems of Conservation Laws 1 written by Denis Serre. This book was released on 1999-05-27. Available in PDF, EPUB and Kindle. Book excerpt: 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 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.

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