Transport Equations And Multi D Hyperbolic Conservation Laws
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| Author | : Luigi Ambrosio |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 141 |
| Release | : 2008-02-17 |
| Genre | : Mathematics |
| ISBN | : 3540767819 |
The theory of nonlinear hyperbolic equations in several space dimensions has recently obtained remarkable achievements. This volume provides an up-to-date overview of the status and perspectives of two areas of research in PDEs, related to hyperbolic conservation laws. The captivating volume contains surveys of recent deep results and provides an overview of further developments and related open problems. Readers should have basic knowledge of PDE and measure theory.
| Author | : Camillo De Lellis |
| Publisher | : |
| Total Pages | : 96 |
| Release | : 2006 |
| Genre | : |
| ISBN | : |
| Author | : Alberto Bressan |
| Publisher | : Springer |
| Total Pages | : 491 |
| Release | : 2011-04-26 |
| Genre | : Mathematics |
| ISBN | : 9781441995551 |
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 | : Helge Holden |
| Publisher | : Springer |
| Total Pages | : 521 |
| Release | : 2015-12-10 |
| Genre | : Mathematics |
| ISBN | : 3662475073 |
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 | : Peter D. Lax |
| Publisher | : SIAM |
| Total Pages | : 53 |
| Release | : 1973-01-01 |
| Genre | : Technology & Engineering |
| ISBN | : 9781611970562 |
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 | : Yuxi Zheng |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 324 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461201411 |
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.
| Author | : Constantine M. Dafermos |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 636 |
| Release | : 2006-01-16 |
| Genre | : Mathematics |
| ISBN | : 3540290893 |
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 | : Philippe G. LeFloch |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 1010 |
| Release | : 2002-07-01 |
| Genre | : Mathematics |
| ISBN | : 9783764366872 |
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.
| Author | : Jean-michel Coron |
| Publisher | : World Scientific |
| Total Pages | : 395 |
| Release | : 2019-01-08 |
| Genre | : Mathematics |
| ISBN | : 9813276193 |
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.
| Author | : C.M. Dafermos |
| Publisher | : Elsevier |
| Total Pages | : 677 |
| Release | : 2005-10-05 |
| Genre | : Mathematics |
| ISBN | : 0080461387 |
The aim of this Handbook is to acquaint the reader with the current status of the theory of evolutionary partial differential equations, and with some of its applications. Evolutionary partial differential equations made their first appearance in the 18th century, in the endeavor to understand the motion of fluids and other continuous media. The active research effort over the span of two centuries, combined with the wide variety of physical phenomena that had to be explained, has resulted in an enormous body of literature. Any attempt to produce a comprehensive survey would be futile. The aim here is to collect review articles, written by leading experts, which will highlight the present and expected future directions of development of the field. The emphasis will be on nonlinear equations, which pose the most challenging problems today. . Volume I of this Handbook does focus on the abstract theory of evolutionary equations. . Volume 2 considers more concrete problems relating to specific applications. . Together they provide a panorama of this amazingly complex and rapidly developing branch of mathematics.
