Admissible Solutions of Hyperbolic Conservation Laws PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Admissible Solutions of Hyperbolic Conservation Laws PDF full book. Access full book title Admissible Solutions of Hyperbolic Conservation Laws by Tai-Ping Liu. Download full books in PDF and EPUB format.
Author: Tai-Ping Liu
Publisher: American Mathematical Soc.
ISBN: 0821822403
Category : Conservation laws
Languages : en
Pages : 86
Get Book Here
Book Description
We consider a system of n conservation laws: [partial derivative/boundary/degree of a polynomial symbol]∂u [over] [partial derivative/boundary/degree of a polynomial symbol]∂t + [partial derivative/boundary/degree of a polynomial symbol]∂f(u) [over] [partial derivative/boundary/degree of a polynomial symbol]∂x = 0. The system is assumed to be strictly hyperbolic, but not necessarily genuinely nonlinear in the sense of Peter Lax (Hyperbolic systems of conservation laws, 1957). Our purpose is to study the regularity, large-time behavior and the approximation of the solution of the initial-value problem. Our analysis is based on the random choice method, using the solution of the Riemann problem, as building blocks.
Author: Tai-Ping Liu
Publisher: American Mathematical Soc.
ISBN: 0821822403
Category : Conservation laws
Languages : en
Pages : 86
Get Book Here
Book Description
We consider a system of n conservation laws: [partial derivative/boundary/degree of a polynomial symbol]∂u [over] [partial derivative/boundary/degree of a polynomial symbol]∂t + [partial derivative/boundary/degree of a polynomial symbol]∂f(u) [over] [partial derivative/boundary/degree of a polynomial symbol]∂x = 0. The system is assumed to be strictly hyperbolic, but not necessarily genuinely nonlinear in the sense of Peter Lax (Hyperbolic systems of conservation laws, 1957). Our purpose is to study the regularity, large-time behavior and the approximation of the solution of the initial-value problem. Our analysis is based on the random choice method, using the solution of the Riemann problem, as building blocks.
Author: Peter D. Lax
Publisher: SIAM
ISBN: 0898711770
Category : Technology & Engineering
Languages : en
Pages : 55
Get Book Here
Book Description
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.
Author: Constantine M. Dafermos
Publisher: Springer Science & Business Media
ISBN: 3540290893
Category : Mathematics
Languages : en
Pages : 636
Get Book Here
Book Description
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: LEVEQUE
Publisher: Birkhäuser
ISBN: 3034851162
Category : Science
Languages : en
Pages : 221
Get Book Here
Book Description
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.
Author: Barbara Lee Keyfitz
Publisher: American Mathematical Soc.
ISBN: 0821850695
Category : Mathematics
Languages : en
Pages : 148
Get Book Here
Book Description
The area of nonstrictly hyperbolic conservation laws is emerging as an important field, not only because it developed from applications of current interest, such as reservoir simulation, visco-elasticity, and multiphase flow, but also because the subject raises interesting mathematical questions of well-posedness, the structure of solutions, and admissibility criteria for weak solutions. The papers in this collection are based on talks presented at an AMS Special Session, held in Anaheim, California, in January 1985. Requiring some background in conservation laws, this collection will be of interest to research mathematicians working in the field of nonstrictly hyperbolic partial differential equations, as well as students who are learning the area and are looking for new applications and challenging problems in this field. The collection provides an overview of the field, examples of applications, descriptions of available techniques, and a bibliography of the literature.
Author: A.G. Kulikovskii
Publisher: CRC Press
ISBN: 1482273993
Category : Mathematics
Languages : en
Pages : 555
Get Book Here
Book Description
This important new book sets forth a comprehensive description of various mathematical aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations. The authors present the material in the context of the important mechanical applications of such systems, including the Euler equations of gas dynamics,
Author: J.M. Ball
Publisher: Springer Science & Business Media
ISBN: 9400971893
Category : Mathematics
Languages : en
Pages : 476
Get Book Here
Book Description
This volume contains the proceedings of a NATO/London Mathematical Society Advanced Study Institute held in Oxford from 25 July - 7 August 1982. The institute concerned the theory and applications of systems of nonlinear partial differential equations, with emphasis on techniques appropriate to systems of more than one equation. Most of the lecturers and participants were analysts specializing in partial differential equations, but also present were a number of numerical analysts, workers in mechanics, and other applied mathematicians. The organizing committee for the institute was J.M. Ball (Heriot-Watt), T.B. Benjamin (Oxford), J. Carr (Heriot-Watt), C.M. Dafermos (Brown), S. Hildebrandt (Bonn) and J.S. pym (Sheffield) . The programme of the institute consisted of a number of courses of expository lectures, together with special sessions on different topics. It is a pleasure to thank all the lecturers for the care they took in the preparation of their talks, and S.S. Antman, A.J. Chorin, J.K. Hale and J.E. Marsden for the organization of their special sessions. The institute was made possible by financial support from NATO, the London Mathematical Society, the u.S. Army Research Office, the u.S. Army European Research Office, and the u.S. National Science Foundation. The lectures were held in the Mathematical Institute of the University of Oxford, and residential accommodation was provided at Hertford College.
Author: Alberto Bressan
Publisher: Oxford University Press, USA
ISBN: 9780198507000
Category : Mathematics
Languages : en
Pages : 270
Get Book Here
Book Description
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: Joel Smoller
Publisher: Springer Science & Business Media
ISBN: 1468401521
Category : Science
Languages : en
Pages : 596
Get Book Here
Book Description
. . . the progress of physics will to a large extent depend on the progress of nonlinear mathe matics, of methods to solve nonlinear equations . . . and therefore we can learn by comparing different nonlinear problems. WERNER HEISENBERG I undertook to write this book for two reasons. First, I wanted to make easily available the basics of both the theory of hyperbolic conservation laws and the theory of systems of reaction-diffusion equations, including the generalized Morse theory as developed by C. Conley. These important subjects seem difficult to learn since the results are scattered throughout the research journals. 1 Second, I feel that there is a need to present the modern methods and ideas in these fields to a wider audience than just mathe maticians. Thus, the book has some rather sophisticated aspects to it, as well as certain textbook aspects. The latter serve to explain, somewhat, the reason that a book with the title Shock Waves and Reaction-Diffusion Equations has the first nine chapters devoted to linear partial differential equations. More precisely, I have found from my classroom experience that it is far easier to grasp the subtleties of nonlinear partial differential equations after one has an understanding of the basic notions in the linear theory. This book is divided into four main parts: linear theory, reaction diffusion equations, shock wave theory, and the Conley index, in that order. Thus, the text begins with a discussion of ill-posed problems.
Author: Philippe G. LeFloch
Publisher: Springer Science & Business Media
ISBN: 9783764366872
Category : Mathematics
Languages : en
Pages : 1010
Get Book Here
Book Description
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.
