Hyperbolic Conservation Laws And The Compensated Compactness Method PDF Download
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Author | : Yunguang Lu |
Publisher | : CRC Press |
Total Pages | : 170 |
Release | : 2002-09-27 |
Genre | : Mathematics |
ISBN | : 1000738094 |
Download Hyperbolic Conservation Laws and the Compensated Compactness Method Book in PDF, ePub and Kindle
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
Author | : C. Dafermos |
Publisher | : Springer Science & Business Media |
Total Pages | : 402 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 1461386896 |
Download Oscillation Theory, Computation, and Methods of Compensated Compactness Book in PDF, ePub and Kindle
This IMA Volume in Mathematics and its Applications Oscillation Theory, Computation, and Methods of Compensated Compactness represents the proceedings of a workshop which was an integral part of the 1984-85 IMA program on CONTINUUM PHYSICS AND PARTIAL DIFFERENTIAL EQUATIONS. We are grateful to the Scientific Committee: J.L. Ericksen D. Kinderlehrer H. Brezis C. Dafermos for their dedication and hard work in developing an imaginative, stimulating, and productive year-long program. George R. Sell Hans Weinberger PREFACE Historically, one of the most important prohlems in continuum mechanics has been the treatment of nonlinear hyperbolic systems of conservation laws. Thp. importance of these systems lies in the fact that the underlyinq equ~tions of mass, momentum, and energy are descrihed by conservation laws. Their nonlinearity and hyperbolicity are consequences of some cornmon constitutive relations, for example, in an ideal gas. The I.M.A. Workshop on "Osci 11 at i on theory. computat i on, and methods of com pensated compactness" brought together scientists from both the analytical and numerical sides of conservation law research. The goal was to examine recent trends in the investigation of systems of conservation laws and in particular to focus on the roles of dispersive and diffusive limits for singularily perturbed conservation laws. Special attention was devoted to the new ideas of compen sated compactness and oscillation theory.
Author | : J.M. Ball |
Publisher | : Springer Science & Business Media |
Total Pages | : 476 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9400971893 |
Download Systems of Nonlinear Partial Differential Equations Book in PDF, ePub and Kindle
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 | : Eitan Tadmor |
Publisher | : American Mathematical Soc. |
Total Pages | : 361 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 0821847295 |
Download Hyperbolic Problems: Theory, Numerics and Applications Book in PDF, ePub and Kindle
The International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 'HYP2008', was held at the University of Maryland from June 9-13, 2008. This book, the first in a two-part volume, contains nineteen papers based on plenary and invited talks presented at the conference.
Author | : Ling Hsiao |
Publisher | : American Mathematical Soc. |
Total Pages | : 260 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 0821819658 |
Download Some Current Topics on Nonlinear Conservation Laws Book in PDF, ePub and Kindle
This volume resulted from a year-long program at the Morningside Center of Mathematics at the Academia Sinica in Beijing. It presents an overview of nonlinear conversation laws and introduces developments in this expanding field. Zhouping Xin's introductory overview of the subject is followed by lecture notes of leading experts who have made fundamental contributions to this field of research. A. Bressan's theory of $-well-posedness for entropy weak solutions to systems of nonlinear hyperbolic conversation laws in the class of viscosity solutions is one of the most important results in the past two decades; G. Chen discusses weak convergence methods and various applications to many problems; P. Degond details mathematical modelling of semi-conductor devices; B. Perthame describes the theory of asymptotic equivalence between conservation laws and singular kinetic equations; Z. Xin outlines the recent development of the vanishing viscosity problem and nonlinear stability of elementary wave-a major focus of research in the last decade; and the volume concludes with Y. Zheng's lecture on incompressible fluid dynamics. This collection of lectures represents previously unpublished expository and research results of experts in nonlinear conservation laws and is an excellent reference for researchers and advanced graduate students in the areas of nonlinear partial differential equations and nonlinear analysis. Titles in this series are co-published with International Press, Cambridge, MA.
Author | : Giuseppe Maria Coclite |
Publisher | : Springer Nature |
Total Pages | : 153 |
Release | : |
Genre | : |
ISBN | : 9819739845 |
Download Scalar Conservation Laws Book in PDF, ePub and Kindle
Author | : Constantine M. Dafermos |
Publisher | : Springer Science & Business Media |
Total Pages | : 710 |
Release | : 2009-12-12 |
Genre | : Mathematics |
ISBN | : 3642040489 |
Download Hyperbolic Conservation Laws in Continuum Physics Book in PDF, ePub and Kindle
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
Author | : C. M. Dafermos |
Publisher | : 清华大学出版社有限公司 |
Total Pages | : 466 |
Release | : 2005 |
Genre | : Conservation laws (Physics) |
ISBN | : 9787302102038 |
Download 连续介质物理中的双曲守恒律(天元基金影印系列丛书) Book in PDF, ePub and Kindle
Author | : Orhan Mehmetoglu |
Publisher | : |
Total Pages | : |
Release | : 2012 |
Genre | : |
ISBN | : |
Download Stability and Convergence of High Order Numerical Methods for Nonlinear Hyperbolic Conservation Laws Book in PDF, ePub and Kindle
Recently there have been numerous advances in the development of numerical algorithms to solve conservation laws. Even though the analytical theory (existence-uniqueness) is complete in the case of scalar conservation laws, there are many numerically robust methods for which the question of convergence and error estimates are still open. Usually high order schemes are constructed to be Total Variation Diminishing (TVD) which only guarantees convergence of such schemes to a weak solution. The standard approach in proving convergence to the entropy solution is to try to establish cell entropy inequalities. However, this typically requires additional non-homogeneous limitations on the numerical method, which reduces the modified scheme to first order when the mesh is refined. There are only a few results on the convergence which do not impose such limitations and all of them assume some smoothness on the initial data in addition to L[^infinity] bound. The Nessyahu-Tadmor (NT) scheme is a typical example of a high order scheme. It is a simple yet robust second order non-oscillatory scheme, which relies on a non-linear piecewise linear reconstruction. A standard reconstruction choice is based on the so-called minmod limiter which gives a maximum principle for the scheme. Unfortunately, this limiter reduces the reconstruction to first order at local extrema. Numerical evidence suggests that this limitation is not necessary. By using MAPR-like limiters, one can allow local nonlinear reconstructions which do not reduce to first order at local extrema. However, use of such limiters requires a new approach when trying to prove a maximum principle for the scheme. It is also well known that the NT scheme does not satisfy the so-called strict cell entropy inequalities, which is the main difficulty in proving convergence to the entropy solution. In this work, the NT scheme with MAPR-like limiters is considered. A maximum principle result for a conservation law with any Lipschitz flux and also with any k-monotone flux is proven. Using this result it is also proven that in the case of strictly convex flux, the NT scheme with a properly selected MAPR-like limiter satisfies an one-sided Lipschitz stability estimate. As a result, convergence to the unique entropy solution when the initial data satisfies the so-called one-sided Lipschitz condition is obtained. Finally, compensated compactness arguments are employed to prove that for any bounded initial data, the NT scheme based on a MAPR-like limiter converges strongly on compact sets to the unique entropy solution of the conservation law with a strictly convex flux.
Author | : Robert Byron Lowrie |
Publisher | : |
Total Pages | : 412 |
Release | : 1996 |
Genre | : |
ISBN | : |
Download Compact Higher-order Numerical Methods for Hyperbolic Conservation Laws Book in PDF, ePub and Kindle