Hyperbolic Conservation Laws And Related Analysis With Applications

Author : Gui-Qiang G. Chen,Helge Holden,Kenneth H. Karlsen
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 47,7 Mb
Release : 2013-09-18
Category : Mathematics
ISBN : 9783642390074

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Hyperbolic Conservation Laws and Related Analysis with Applications by Gui-Qiang G. Chen,Helge Holden,Kenneth H. Karlsen Pdf

This book presents thirteen papers, representing the most significant advances and current trends in nonlinear hyperbolic conservation laws and related analysis with applications. Topics covered include a survey on multidimensional systems of conservation laws as well as novel results on liquid crystals, conservation laws with discontinuous flux functions, and applications to sedimentation. Also included are articles on recent advances in the Euler equations and the Navier-Stokes-Fourier-Poisson system, in addition to new results on collective phenomena described by the Cucker-Smale model. The Workshop on Hyperbolic Conservation Laws and Related Analysis with Applications at the International Centre for Mathematical Sciences (Edinburgh, UK) held in Edinburgh, September 2011, produced this fine collection of original research and survey articles. Many leading mathematicians attended the event and submitted their contributions for this volume. It is addressed to researchers and graduate students interested in partial differential equations and related analysis with applications.

Author : Gui-Qiang G. Chen,Helge Holden,Kenneth H. Karlsen
Publisher : Unknown
Page : 396 pages
File Size : 47,5 Mb
Release : 2013-10-31
Category : Electronic
ISBN : 3642390080

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Hyperbolic Conservation Laws and Related Analysis with Applications by Gui-Qiang G. Chen,Helge Holden,Kenneth H. Karlsen Pdf

Author : Alberto Bressan,Gui-Qiang G. Chen,Marta Lewicka,Dehua Wang
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 44,7 Mb
Release : 2011-04-19
Category : Mathematics
ISBN : 9781441995544

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Nonlinear Conservation Laws and Applications by Alberto Bressan,Gui-Qiang G. Chen,Marta Lewicka,Dehua Wang Pdf

This volume contains the proceedings of the Summer Program on Nonlinear Conservation Laws and Applications held at the IMA on July 13--31, 2009. Hyperbolic conservation laws is a classical subject, which has experienced vigorous growth in recent years. The present collection provides a timely survey of the state of the art in this exciting field, and a comprehensive outlook on open problems. Contributions of more theoretical nature cover the following topics: global existence and uniqueness theory of one-dimensional systems, multidimensional conservation laws in several space variables and approximations of their solutions, mathematical analysis of fluid motion, stability and dynamics of viscous shock waves, singular limits for viscous systems, basic principles in the modeling of turbulent mixing, transonic flows past an obstacle and a fluid dynamic approach for isometric embedding in geometry, models of nonlinear elasticity, the Monge problem, and transport equations with rough coefficients. In addition, there are a number of papers devoted to applications. These include: models of blood flow, self-gravitating compressible fluids, granular flow, charge transport in fluids, and the modeling and control of traffic flow on networks.

Author : Jan S. Hesthaven
Publisher : SIAM
Page : 571 pages
File Size : 45,6 Mb
Release : 2018-01-30
Category : Science
ISBN : 9781611975093

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Numerical Methods for Conservation Laws by Jan S. Hesthaven Pdf

Conservation laws are the mathematical expression of the principles of conservation and provide effective and accurate predictive models of our physical world. Although intense research activity during the last decades has led to substantial advances in the development of powerful computational methods for conservation laws, their solution remains a challenge and many questions are left open; thus it is an active and fruitful area of research. Numerical Methods for Conservation Laws: From Analysis to Algorithms: offers the first comprehensive introduction to modern computational methods and their analysis for hyperbolic conservation laws, building on intense research activities for more than four decades of development; discusses classic results on monotone and finite difference/finite volume schemes, but emphasizes the successful development of high-order accurate methods for hyperbolic conservation laws; addresses modern concepts of TVD and entropy stability, strongly stable Runge-Kutta schemes, and limiter-based methods before discussing essentially nonoscillatory schemes, discontinuous Galerkin methods, and spectral methods; explores algorithmic aspects of these methods, emphasizing one- and two-dimensional problems and the development and analysis of an extensive range of methods; includes MATLAB software with which all main methods and computational results in the book can be reproduced; and demonstrates the performance of many methods on a set of benchmark problems to allow direct comparisons. Code and other supplemental material are available online at www.siam.org/books/cs18.

Author : Helge Holden,Nils Henrik Risebro
Publisher : Springer
Page : 517 pages
File Size : 43,9 Mb
Release : 2015-12-10
Category : Mathematics
ISBN : 9783662475072

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Front Tracking for Hyperbolic Conservation Laws by Helge Holden,Nils Henrik Risebro Pdf

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.

Author : Heinrich Freistuhler
Publisher : CRC Press
Page : 276 pages
File Size : 52,9 Mb
Release : 1998-12-30
Category : Mathematics
ISBN : 0849306442

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Analysis of Systems of Conservation Laws by Heinrich Freistuhler Pdf

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.

Author : Alberto Bressan
Publisher : Oxford University Press, USA
Page : 270 pages
File Size : 47,7 Mb
Release : 2000
Category : Mathematics
ISBN : 0198507003

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Hyperbolic Systems of Conservation Laws by Alberto Bressan Pdf

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.

Author : Constantine M. Dafermos
Publisher : Springer
Page : 826 pages
File Size : 43,7 Mb
Release : 2016-05-26
Category : Mathematics
ISBN : 9783662494516

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Hyperbolic Conservation Laws in Continuum Physics by Constantine M. Dafermos Pdf

This is a masterly exposition and an encyclopedic presentation of the theory of hyperbolic conservation laws. It illustrates the essential role of continuum thermodynamics in providing motivation and direction for the development of the mathematical theory while also serving as the principal source of applications. The reader is expected to have a certain mathematical sophistication and to be familiar with (at least) the rudiments of analysis and the qualitative theory of partial differential equations, whereas prior exposure to continuum physics is not required. The target group of readers would consist of (a) experts in the mathematical theory of hyperbolic systems of conservation laws who wish to learn about the connection with classical physics; (b) specialists in continuum mechanics who may need analytical tools; (c) experts in numerical analysis who wish to learn the underlying mathematical theory; and (d) analysts and graduate students who seek introduction to the theory of hyperbolic systems of conservation laws. This new edition places increased emphasis on hyperbolic systems of balance laws with dissipative source, modeling relaxation phenomena. It also presents an account of recent developments on the Euler equations of compressible gas dynamics. Furthermore, the presentation of a number of topics in the previous edition has been revised, expanded and brought up to date, and has been enriched with new applications to elasticity and differential geometry. The bibliography, also expanded and updated, now comprises close to two thousand titles. From the reviews of the 3rd edition: "This is the third edition of the famous book by C.M. Dafermos. His masterly written book is, surely, the most complete exposition in the subject." Evgeniy Panov, Zentralblatt MATH "A monumental book encompassing all aspects of the mathematical theory of hyperbolic conservation laws, widely recognized as the "Bible" on the subject." Philippe G. LeFloch, Math. Reviews

Author : Edwige Godlewski,Pierre-Arnaud Raviart
Publisher : Springer Nature
Page : 846 pages
File Size : 43,5 Mb
Release : 2021-08-28
Category : Mathematics
ISBN : 9781071613443

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Numerical Approximation of Hyperbolic Systems of Conservation Laws by Edwige Godlewski,Pierre-Arnaud Raviart Pdf

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.

Author : Constantine M. Dafermos
Publisher : Springer Science & Business Media
Page : 636 pages
File Size : 42,9 Mb
Release : 2006-01-16
Category : Mathematics
ISBN : 9783540290896

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Hyperbolic Conservation Laws in Continuum Physics by Constantine M. Dafermos Pdf

This is a lucid and authoritative exposition of the mathematical theory of hyperbolic system laws. The second edition contains a new chapter recounting exciting recent developments on the vanishing viscosity method. Numerous new sections introduce newly derived results. From the reviews: "The author is known as one of the leading experts in the field. His masterly written book is, surely, the most complete exposition in the subject of conservations laws." --Zentralblatt MATH

Author : G Geymonat
Publisher : World Scientific
Page : 190 pages
File Size : 45,7 Mb
Release : 1987-02-01
Category : Mathematics
ISBN : 9789814507851

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Partial Differential Equations Of Hyperbolic Type And Applications by G Geymonat Pdf

This book introduces the general aspects of hyperbolic conservation laws and their numerical approximation using some of the most modern tools: spectral methods, unstructured meshes and λ-formulation. The applications of these methods are found in some significant examples such as the Euler equations. This book, a collection of articles by the best authors in the field, exposes the reader to the frontier of the research and many open problems.

Author : Barbara Lee Keyfitz
Publisher : American Mathematical Soc.
Page : 133 pages
File Size : 55,9 Mb
Release : 1987
Category : Science
ISBN : 9780821850695

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Nonstrictly Hyperbolic Conservation Laws by Barbara Lee Keyfitz Pdf

Author : Tai-Ping Liu
Publisher : SIAM
Page : 78 pages
File Size : 42,8 Mb
Release : 2000-01-01
Category : Mathematics
ISBN : 9780898714364

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Hyperbolic and Viscous Conservation Laws by Tai-Ping Liu Pdf

An in-depth analysis of wave interactions for general systems of hyperbolic and viscous conservation laws.

Author : Jean-Michel Coron,Daqian Li,Yachun Li
Publisher : Unknown
Page : 128 pages
File Size : 51,8 Mb
Release : 2018
Category : MATHEMATICS
ISBN : 9813276185

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One-dimensional Hyperbolic Conservation Laws and Their Applications by Jean-Michel Coron,Daqian Li,Yachun Li Pdf

Author : LEVEQUE
Publisher : Birkhäuser
Page : 214 pages
File Size : 50,7 Mb
Release : 2013-11-11
Category : Science
ISBN : 9783034851169

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Numerical Methods for Conservation Laws by LEVEQUE Pdf

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. vVithout 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.