Systems Of Conservation Laws 2

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Systems of Conservation Laws 2

Author : Denis Serre
Publisher : Cambridge University Press
Page : 286 pages
File Size : 44,7 Mb
Release : 1999
Category : Law
ISBN : 0521633303

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Systems of Conservation Laws 2 by Denis Serre Pdf

A graduate text on mathematical theory of conservation laws and partial differential equations.

Systems of Conservation Laws 1

Author : Denis Serre
Publisher : Cambridge University Press
Page : 290 pages
File Size : 48,5 Mb
Release : 1999-05-27
Category : Mathematics
ISBN : 1139425412

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Systems of Conservation Laws 1 by Denis Serre Pdf

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.

Numerical Approximation of Hyperbolic Systems of Conservation Laws

Author : Edwige Godlewski,Pierre-Arnaud Raviart
Publisher : Springer Nature
Page : 846 pages
File Size : 40,9 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.

Hyperbolic Systems of Conservation Laws

Author : Philippe G. LeFloch
Publisher : Springer Science & Business Media
Page : 1010 pages
File Size : 45,8 Mb
Release : 2002-07-01
Category : Mathematics
ISBN : 3764366877

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Hyperbolic Systems of Conservation Laws by Philippe G. LeFloch Pdf

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.

Front Tracking for Hyperbolic Conservation Laws

Author : Helge Holden,Nils Henrik Risebro
Publisher : Springer
Page : 517 pages
File Size : 44,9 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.

Numerical Methods for Conservation Laws

Author : LEVEQUE
Publisher : Birkhäuser
Page : 214 pages
File Size : 50,9 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.

Systems of Conservation Laws

Author : Yuxi Zheng
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201410

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Systems of Conservation Laws by Yuxi Zheng Pdf

This work should serve as an introductory text for graduate students and researchers working in the important area of partial differential equations with a focus on problems involving conservation laws. The only requisite for the reader is a knowledge of the elementary theory of partial differential equations. Key features of this work include: * broad range of topics, from the classical treatment to recent results, dealing with solutions to 2D compressible Euler equations * good review of basic concepts (1-D Riemann problems) * concrete solutions presented, with many examples, over 100 illustrations, open problems, and numerical schemes * numerous exercises, comprehensive bibliography and index * appeal to a wide audience of applied mathematicians, graduate students, physicists, and engineers Written in a clear, accessible style, the book emphasizes more recent results that will prepare readers to meet modern challenges in the subject, that is, to carry out theoretical, numerical, and asymptotical analysis.

Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables

Author : A. Majda
Publisher : Springer Science & Business Media
Page : 167 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461211167

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Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables by A. Majda Pdf

Conservation laws arise from the modeling of physical processes through the following three steps: 1) The appropriate physical balance laws are derived for m-phy- t cal quantities, ul""'~ with u = (ul' ... ,u ) and u(x,t) defined m for x = (xl""'~) E RN (N = 1,2, or 3), t > 0 and with the values m u(x,t) lying in an open subset, G, of R , the state space. The state space G arises because physical quantities such as the density or total energy should always be positive; thus the values of u are often con strained to an open set G. 2) The flux functions appearing in these balance laws are idealized through prescribed nonlinear functions, F.(u), mapping G into J j = 1, ..• ,N while source terms are defined by S(u,x,t) with S a given smooth function of these arguments with values in Rm. In parti- lar, the detailed microscopic effects of diffusion and dissipation are ignored. 3) A generalized version of the principle of virtual work is applied (see Antman [1]). The formal result of applying the three steps (1)-(3) is that the m physical quantities u define a weak solution of an m x m system of conservation laws, o I + N(Wt'u + r W ·F.(u) + W·S(u,x,t))dxdt (1.1) R xR j=l Xj J for all W E C~(RN x R+), W(x,t) E Rm.

Nonlinear Conservation Laws and Applications

Author : Alberto Bressan,Gui-Qiang G. Chen,Marta Lewicka,Dehua Wang
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 54,6 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.

Hyperbolic Systems of Conservation Laws

Author : Alberto Bressan
Publisher : Oxford University Press, USA
Page : 270 pages
File Size : 40,5 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.

Numerical Methods for Conservation Laws

Author : Jan S. Hesthaven
Publisher : SIAM
Page : 570 pages
File Size : 41,6 Mb
Release : 2018-01-30
Category : Science
ISBN : 9781611975109

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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 will be available online at publication.

Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves

Author : Peter D. Lax
Publisher : SIAM
Page : 55 pages
File Size : 46,9 Mb
Release : 1973-01-01
Category : Technology & Engineering
ISBN : 9780898711776

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Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves by Peter D. Lax Pdf

This book deals with the mathematical side of the theory of shock waves. The author presents what is known about the existence and uniqueness of generalized solutions of the initial value problem subject to the entropy conditions. The subtle dissipation introduced by the entropy condition is investigated and the slow decay in signal strength it causes is shown.

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 : 51,9 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.

Hyperbolic Conservation Laws and the Compensated Compactness Method

Author : Yunguang Lu
Publisher : CRC Press
Page : 170 pages
File Size : 48,9 Mb
Release : 2002-09-27
Category : Mathematics
ISBN : 9781000738094

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Hyperbolic Conservation Laws and the Compensated Compactness Method by Yunguang Lu Pdf

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

Well-posedness for General 2 X 2 Systems of Conservation Laws

Author : Fabio Ancona,Andrea Marson
Publisher : American Mathematical Soc.
Page : 170 pages
File Size : 45,5 Mb
Release : 2004
Category : Mathematics
ISBN : 1470403994

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Well-posedness for General 2 X 2 Systems of Conservation Laws by Fabio Ancona,Andrea Marson Pdf

Introduction Preliminaries Outline of the proof The algorithm Basic interaction estimates Bounds on the total variation and on the interaction potential Estimates on the number of discontinuities Estimates on shift differentials Completion of the proof Conclusion Bibliography.