One Dimensional Hyperbolic Conservation Laws And Their Applications

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One-dimensional Hyperbolic Conservation Laws And Their Applications

Jean-michel Coron,Tatsien Li,Yachun Li
One dimensional Hyperbolic Conservation Laws And Their Applications Book PDF

Author : Jean-michel Coron,Tatsien Li,Yachun Li
Publisher : World Scientific
Page : 395 pages
File Size : 55,7 Mb
Release : 2019-01-08
Category : Mathematics
ISBN : 9789813276192

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One-dimensional Hyperbolic Conservation Laws And Their Applications by Jean-michel Coron,Tatsien Li,Yachun Li Pdf

This book is a collection of lecture notes for the LIASFMA Shanghai Summer School on 'One-dimensional Hyperbolic Conservation Laws and Their Applications' which was held during August 16 to August 27, 2015 at Shanghai Jiao Tong University, Shanghai, China. This summer school is one of the activities promoted by Sino-French International Associate Laboratory in Applied Mathematics (LIASFMA in short). LIASFMA was established jointly by eight institutions in China and France in 2014, which is aimed at providing a platform for some of the leading French and Chinese mathematicians to conduct in-depth researches, extensive exchanges, and student training in the field of applied mathematics. This summer school has the privilege of being the first summer school of the newly established LIASFMA, which makes it significant.

Hyperbolic Systems of Conservation Laws

Alberto Bressan
Hyperbolic Systems of Conservation Laws Book PDF

Author : Alberto Bressan
Publisher : Oxford University Press, USA
Page : 270 pages
File Size : 43,7 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.

Stability and Boundary Stabilization of 1-D Hyperbolic Systems

Georges Bastin,Jean-Michel Coron
Stability and Boundary Stabilization of 1 D Hyperbolic Systems Book PDF

Author : Georges Bastin,Jean-Michel Coron
Publisher : Birkhäuser
Page : 307 pages
File Size : 50,9 Mb
Release : 2016-07-26
Category : Mathematics
ISBN : 9783319320625

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Stability and Boundary Stabilization of 1-D Hyperbolic Systems by Georges Bastin,Jean-Michel Coron Pdf

This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the concepts in whichever setting is most familiar to them. With these examples, it also illustrates how control boundary conditions may be defined for the most commonly used control devices. The authors begin with the simple case of systems of two linear conservation laws and then consider the stability of systems under more general boundary conditions that may be differential, nonlinear, or switching. They then extend their discussion to the case of nonlinear conservation laws and demonstrate the use of Lyapunov functions in this type of analysis. Systems of balance laws are considered next, starting with the linear variety before they move on to more general cases of nonlinear ones. They go on to show how the problem of boundary stabilization of systems of two balance laws by both full-state and dynamic output feedback in observer-controller form is solved by using a “backstepping” method, in which the gains of the feedback laws are solutions of an associated system of linear hyperbolic PDEs. The final chapter presents a case study on the control of navigable rivers to emphasize the main technological features that may occur in real live applications of boundary feedback control. Stability and Boundary Stabilization of 1-D Hyperbolic Systems will be of interest to graduate students and researchers in applied mathematics and control engineering. The wide range of applications it discusses will help it to have as broad an appeal within these groups as possible.

Systems of Conservation Laws

Yuxi Zheng
Systems of Conservation Laws Book PDF

Author : Yuxi Zheng
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 44,7 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.

Nonlinear Conservation Laws and Applications

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

Author : Alberto Bressan,Gui-Qiang G. Chen,Marta Lewicka,Dehua Wang
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 53,8 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.

Front Tracking for Hyperbolic Conservation Laws

Helge Holden,Nils Henrik Risebro
Front Tracking for Hyperbolic Conservation Laws Book PDF

Author : Helge Holden,Nils Henrik Risebro
Publisher : Springer
Page : 517 pages
File Size : 53,6 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 Approximation of Hyperbolic Systems of Conservation Laws

Edwige Godlewski,Pierre-Arnaud Raviart
Numerical Approximation of Hyperbolic Systems of Conservation Laws Book PDF

Author : Edwige Godlewski,Pierre-Arnaud Raviart
Publisher : Springer Nature
Page : 846 pages
File Size : 53,5 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.

Numerical Methods for Conservation Laws

Jan S. Hesthaven
Numerical Methods for Conservation Laws Book PDF

Author : Jan S. Hesthaven
Publisher : SIAM
Page : 570 pages
File Size : 42,6 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 Problems: Theory, Numerics, Applications

Heinrich Freistühler,Gerald Warnecke
Hyperbolic Problems Theory Numerics Applications Book PDF

Author : Heinrich Freistühler,Gerald Warnecke
Publisher : Birkhäuser
Page : 471 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883726

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Hyperbolic Problems: Theory, Numerics, Applications by Heinrich Freistühler,Gerald Warnecke Pdf

Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics. The mathematical theory of hyperbolic equations has recently made considerable progress. Accurate and efficient numerical schemes for computation have been and are being further developed. This two-volume set of conference proceedings contains about 100 refereed and carefully selected papers. The books are intended for researchers and graduate students in mathematics, science and engineering interested in the most recent results in theory and practice of hyperbolic problems. Applications touched in these proceedings concern one-phase and multiphase fluid flow, phase transitions, shallow water dynamics, elasticity, extended thermodynamics, electromagnetism, classical and relativistic magnetohydrodynamics, cosmology. Contributions to the abstract theory of hyperbolic systems deal with viscous and relaxation approximations, front tracking and wellposedness, stability of shock profiles and multi-shock patterns, traveling fronts for transport equations. Numerically oriented articles study finite difference, finite volume, and finite element schemes, adaptive, multiresolution, and artificial dissipation methods.

Godunov-type Schemes

V. Guinot
Godunov type Schemes Book PDF

Author : V. Guinot
Publisher : Elsevier
Page : 508 pages
File Size : 44,9 Mb
Release : 2003-01-29
Category : Mathematics
ISBN : 0080532586

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Godunov-type Schemes by V. Guinot Pdf

Godunov-type schemes appear as good candidates for the next generation of commercial modelling software packages, the capability of which to handle discontinuous solution will be a basic requirement. It is in the interest of practising engineers and developers to be familiar with the specific features of discontinuous wave propagation problems and to be aware of the possibilities offered by Godunov-type schemes for their solution. This book aims to present the principles of such schemes in a way that is easily understandable to practising engineers. The features of hyperbolic conservation laws and their solutions are presented in the first two chapters. The principles of Godunov-type schemes are outlined in a third chapter. Chapters 4 and 5 cover the application of the original Godunov scheme to scalar laws and to hyperbolic systems of conservation laws respectively. Chapter 6 is devoted to higher-order schemes in one dimension of space. The design of such a scheme is described for the general case and applied to some well-known schemes such as the MUSCL and PPM schemes. Chapter 7 focuses on multidimensional problems. The classical alternate directions and finite volume approaches are presented together with the wave splitting technique that is described in depth with an application to two-dimensional systems. Chapter 8 deals with large-time step algorithms. These include front tracking-based methods, explicit-implicit techniques and the time-line interpolation technique. Three appendices provide notions on accuracy and stability issues, Riemann solvers and the user instructions for the computational codes provided in the enclosed CD-ROM.

Hyperbolic Conservation Laws and Related Analysis with Applications

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

Author : Gui-Qiang G. Chen,Helge Holden,Kenneth H. Karlsen
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 53,7 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.

Front Tracking for Hyperbolic Conservation Laws

Helge Holden,Nils H. Risebro
Front Tracking for Hyperbolic Conservation Laws Book PDF

Author : Helge Holden,Nils H. Risebro
Publisher : Springer
Page : 264 pages
File Size : 50,5 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9783642561399

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

This book presents the theory of hyperbolic conservation laws from basic theory to the forefront of research. The text treats the theory of scalar conservation laws in one dimension in detail, showing the stability of the Cauchy problem using front tracking. The extension to multidimensional scalar conservation laws is obtained using dimensional splitting. The book includes detailed discussion of the recent proof of well-posedness of the Cauchy problem for one-dimensional hyperbolic conservation laws, and a chapter on traditional finite difference methods for hyperbolic conservation laws with error estimates and a section on measure valued solutions.

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

Peter D. Lax
Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves Book PDF

Author : Peter D. Lax
Publisher : SIAM
Page : 55 pages
File Size : 51,7 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 in Continuum Physics

Constantine M. Dafermos
Hyperbolic Conservation Laws in Continuum Physics Book PDF

Author : Constantine M. Dafermos
Publisher : Springer
Page : 710 pages
File Size : 50,7 Mb
Release : 2010-05-27
Category : Mathematics
ISBN : 3642040543

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

The 3rd edition is thoroughly revised, applications are substantially enriched, it includes a new account of the early history of the subject (from 1800 to 1957) and a new chapter recounting the recent solution of open problems of long standing in classical aerodynamics. The bibliography comprises now over fifteen hundred titles. 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

Theory, Numerics and Applications of Hyperbolic Problems I

Christian Klingenberg,Michael Westdickenberg
Theory Numerics and Applications of Hyperbolic Problems I Book PDF

Author : Christian Klingenberg,Michael Westdickenberg
Publisher : Springer
Page : 706 pages
File Size : 45,7 Mb
Release : 2018-06-23
Category : Mathematics
ISBN : 9783319915456

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Theory, Numerics and Applications of Hyperbolic Problems I by Christian Klingenberg,Michael Westdickenberg Pdf

The first of two volumes, this edited proceedings book features research presented at the XVI International Conference on Hyperbolic Problems held in Aachen, Germany in summer 2016. It focuses on the theoretical, applied, and computational aspects of hyperbolic partial differential equations (systems of hyperbolic conservation laws, wave equations, etc.) and of related mathematical models (PDEs of mixed type, kinetic equations, nonlocal or/and discrete models) found in the field of applied sciences.