Nonstrictly Hyperbolic Conservation Laws

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Nonstrictly Hyperbolic Conservation Laws

Barbara Lee Keyfitz,Herbert C. Kranzer
Nonstrictly Hyperbolic Conservation Laws Book PDF

Author : Barbara Lee Keyfitz,Herbert C. Kranzer
Publisher : American Mathematical Soc.
Page : 148 pages
File Size : 55,9 Mb
Release : 1987
Category : Mathematics
ISBN : 9780821850695

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Nonstrictly Hyperbolic Conservation Laws by Barbara Lee Keyfitz,Herbert C. Kranzer Pdf

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.

Nonstrictly Hyperbolic Conservation Laws

Barbara L. Keyfitz,HOUSTON UNIV TX DEPT OF MATHEMATICS.
Nonstrictly Hyperbolic Conservation Laws Book PDF

Author : Barbara L. Keyfitz,HOUSTON UNIV TX DEPT OF MATHEMATICS.
Publisher : Unknown
Page : 7 pages
File Size : 45,8 Mb
Release : 1989
Category : Electronic
ISBN : OCLC:227754735

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Nonstrictly Hyperbolic Conservation Laws by Barbara L. Keyfitz,HOUSTON UNIV TX DEPT OF MATHEMATICS. Pdf

This project has centered on formulating and solving mathematical problems that arise in the study of systems of conservation laws that are not of the classical, strictly hyperbolic type. Potential applications for these results are found in models for three-phases flow in porous media, for compressible two-phase flow, and for flow in elastic and elastoplastic materials (including continuum models for granular flow). Modelling of many different flow processes has led to systems of conservation laws in which the classical assumptions breakdown in a way which leads to distrust of the models. Research in this and allied projects is directed at extending the mathematical theory of conservation laws. The practical goal of this research is to discover which models are well-posed, and, hence, to enable applied scientists to discover which are correct descriptions of various observed instabilities. (JHD).

Analysis of Systems of Conservation Laws

Heinrich Freistuhler
Analysis of Systems of Conservation Laws Book PDF

Author : Heinrich Freistuhler
Publisher : CRC Press
Page : 276 pages
File Size : 55,7 Mb
Release : 1998-12-30
Category : Mathematics
ISBN : 0849306442

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Analysis of Systems of Conservation Laws by Heinrich Freistuhler Pdf

Systems of partial differential equations reflecting conservation laws hold significant relevance to a variety of theoretical and practical applications, including compressible fluid flow, electromagnetism, elasticity theory, and other areas of continuum mechanics. This field of nonlinear analysis is currently experiencing a marked increase in successful research activity. The EU-TMR network "Hyperbolic Systems of Conservation Laws held a summer program offering short courses on the Analysis of Systems of Conservation Laws. This book contains five of the self-contained short courses presented during this program by experts of international reputation. These courses, which address solutions to hyperbolic systems by the front tracking method, non-strictly hyperbolic conservation laws, hyperbolic-elliptic coupled systems, hyperbolic relaxation problems, the stability of nonlinear waves in viscous media and numerics, and more, represent the state of the art of most central aspects of the field.

Hyperbolic Conservation Laws in Continuum Physics

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

Author : Constantine M. Dafermos
Publisher : Springer Science & Business Media
Page : 636 pages
File Size : 52,6 Mb
Release : 2006-01-16
Category : Mathematics
ISBN : 9783540290896

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

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

Nonlinear PDE's, Dynamics and Continuum Physics

J. L. Bona,Katarzyna Saxton,Ralph Saxton
Nonlinear PDE s Dynamics and Continuum Physics Book PDF

Author : J. L. Bona,Katarzyna Saxton,Ralph Saxton
Publisher : American Mathematical Soc.
Page : 270 pages
File Size : 52,7 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821810521

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Nonlinear PDE's, Dynamics and Continuum Physics by J. L. Bona,Katarzyna Saxton,Ralph Saxton Pdf

This volume contains the refereed proceedings of the conference on Nonlinear Partial Differential Equations, Dynamics and Continuum Physics which was held at Mount Holyoke College in Massachusetts, from July 19th to July 23rd, 1998. Models examined derive from a wide range of applications, including elasticity, thermoviscoelasticity, granular media, fluid dynamics, gas dynamics and conservation laws. Mathematical topics include existence theory and stability/instability of traveling waves, asymptotic behavior of solutions to nonlinear wave equations, effects of dissipation, mechanisms of blow-up, well-posedness and regularity, and fractal solutions. The text will be of interest to graduate students and researchers working in nonlinear partial differential equations and applied mathematics.

Hyperbolic Conservation Laws and the Compensated Compactness Method

Yunguang Lu
Hyperbolic Conservation Laws and the Compensated Compactness Method Book PDF

Author : Yunguang Lu
Publisher : CRC Press
Page : 170 pages
File Size : 51,8 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

Hyperbolic Conservation Laws and the Compensated Compactness Method

Yunguang Lu
Hyperbolic Conservation Laws and the Compensated Compactness Method Book PDF

Author : Yunguang Lu
Publisher : CRC Press
Page : 254 pages
File Size : 51,6 Mb
Release : 2002-09-27
Category : Mathematics
ISBN : 9781420035575

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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

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 : 47,8 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 Problems: Theory, Numerics, Applications - Proceedings Of The Fifth International Conference

James Glimm,M J Graham,J W Grove,Bradley J Plohr
Hyperbolic Problems Theory Numerics Applications Proceedings Of The Fifth International Conference Book PDF

Author : James Glimm,M J Graham,J W Grove,Bradley J Plohr
Publisher : World Scientific
Page : 510 pages
File Size : 46,7 Mb
Release : 1996-03-14
Category : Electronic
ISBN : 9789814548588

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Hyperbolic Problems: Theory, Numerics, Applications - Proceedings Of The Fifth International Conference by James Glimm,M J Graham,J W Grove,Bradley J Plohr Pdf

The intellectual center of this proceedings volume is the subject of conservation laws. Conservation laws are the most basic model of many continuum processes, and for this reason they govern the motion of fluids, solids, and plasma. They are basic to the understanding of more complex modeling issues, such as multiphase flow, chemically reacting flow, and non-equilibrium thermodynamics. Equations of this type also arise in novel and unexpected areas, such as the pattern recognition and image processing problem of edge enhancement and detection. The articles in this volume address the entire range of the study of conservation laws, including the fundamental mathematical theory, familiar and novel applications, and the numerical problem of finding effective computational algorithms for the solution of these problems.

Distribution Solutions of Nonlinear Systems of Conservation Laws

Michael Sever
Distribution Solutions of Nonlinear Systems of Conservation Laws Book PDF

Author : Michael Sever
Publisher : American Mathematical Soc.
Page : 178 pages
File Size : 40,9 Mb
Release : 2007
Category : Conservation laws
ISBN : 9780821839904

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Distribution Solutions of Nonlinear Systems of Conservation Laws by Michael Sever Pdf

The local structure of solutions of initial value problems for nonlinear systems of conservation laws is considered. Given large initial data, there exist systems with reasonable structural properties for which standard entropy weak solutions cannot be continued after finite time, but for which weaker solutions, valued as measures at a given time, exist. At any given time, the singularities thus arising admit representation as weak limits of suitable approximate solutions in the space of measures with respect to the space variable. Two distinct classes of singularities have emerged in this context, known as delta-shocks and singular shocks. Notwithstanding the similar form of the singularities, the analysis of delta-shocks is very different from that of singular shocks, as are the systems for which they occur. Roughly speaking, the difference is that for delta-shocks, the density approximations majorize the flux approximations, whereas for singular shocks, the flux approximations blow up faster. As against that admissible singular shocks have viscous structure.

Multidimensional Hyperbolic Problems and Computations

James Glimm,Andrew J. Majda
Multidimensional Hyperbolic Problems and Computations Book PDF

Author : James Glimm,Andrew J. Majda
Publisher : Springer Science & Business Media
Page : 399 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461391210

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Multidimensional Hyperbolic Problems and Computations by James Glimm,Andrew J. Majda Pdf

This IMA Volume in Mathematics and its Applications MULTIDIMENSIONAL HYPERBOLIC PROBLEMS AND COMPUTATIONS is based on the proceedings of a workshop which was an integral part ofthe 1988-89 IMA program on NONLINEAR WAVES. We are grateful to the Scientific Commit tee: James Glimm, Daniel Joseph, Barbara Keyfitz, Andrew Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for planning and implementing an exciting and stimulating year-long program. We especially thank the Work shop Organizers, Andrew Majda and James Glimm, for bringing together many of the major figures in a variety of research fields connected with multidimensional hyperbolic problems. A vner Friedman Willard Miller PREFACE A primary goal of the IMA workshop on Multidimensional Hyperbolic Problems and Computations from April 3-14, 1989 was to emphasize the interdisciplinary nature of contemporary research in this field involving the combination of ideas from the theory of nonlinear partial differential equations, asymptotic methods, numerical computation, and experiments. The twenty-six papers in this volume span a wide cross-section of this research including some papers on the kinetic theory of gases and vortex sheets for incompressible flow in addition to many papers on systems of hyperbolic conservation laws. This volume includes several papers on asymptotic methods such as nonlinear geometric optics, a number of articles applying numerical algorithms such as higher order Godunov methods and front tracking to physical problems along with comparison to experimental data, and also several interesting papers on the rigorous mathematical theory of shock waves.

Nonlinear Hyperbolic Problems

Claude Carasso,Pierre-Arnaud Raviart,Denis Serre
Nonlinear Hyperbolic Problems Book PDF

Author : Claude Carasso,Pierre-Arnaud Raviart,Denis Serre
Publisher : Springer
Page : 356 pages
File Size : 47,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540478058

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Nonlinear Hyperbolic Problems by Claude Carasso,Pierre-Arnaud Raviart,Denis Serre Pdf

The field of nonlinear hyperbolic problems has been expanding very fast over the past few years, and has applications - actual and potential - in aerodynamics, multifluid flows, combustion, detonics amongst other. The difficulties that arise in application are of theoretical as well as numerical nature. In fact, the papers in this volume of proceedings deal to a greater extent with theoretical problems emerging in the resolution of nonlinear hyperbolic systems than with numerical methods. The volume provides an excellent up-to-date review of the current research trends in this area.

Finite Volume Methods for Hyperbolic Problems

Randall J. LeVeque
Finite Volume Methods for Hyperbolic Problems Book PDF

Author : Randall J. LeVeque
Publisher : Cambridge University Press
Page : 582 pages
File Size : 50,9 Mb
Release : 2002-08-26
Category : Mathematics
ISBN : 0521009243

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Finite Volume Methods for Hyperbolic Problems by Randall J. LeVeque Pdf

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Nonlinear Hyperbolic Equations — Theory, Computation Methods, and Applications

Josef Ballmann,Rolf Jeltsch
Nonlinear Hyperbolic Equations Theory Computation Methods and Applications Book PDF

Author : Josef Ballmann,Rolf Jeltsch
Publisher : Springer Science & Business Media
Page : 729 pages
File Size : 43,5 Mb
Release : 2013-03-08
Category : Technology & Engineering
ISBN : 9783322878694

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Nonlinear Hyperbolic Equations — Theory, Computation Methods, and Applications by Josef Ballmann,Rolf Jeltsch Pdf

On the occasion of the International Conference on Nonlinear Hyperbolic Problems held in St. Etienne, France, 1986 it was decided to start a two years cycle of conferences on this very rapidly expanding branch of mathematics and it·s applications in Continuum Mechanics and Aerodynamics. The second conference toolc place in Aachen, FRG, March 14-18, 1988. The number of more than 200 participants from more than 20 countries all over the world and about 100 invited and contributed papers, well balanced between theory, numerical analysis and applications, do not leave any doubt that it was the right decision to start this cycle of conferences, of which the third will be organized in Sweden in 1990. ThiS volume contains sixty eight original papers presented at the conference, twenty two cif them dealing with the mathematical theory, e.g. existence, uniqueness, stability, behaviour of solutions, physical modelling by evolution equations. Twenty two articles in numerical analysis are concerned with stability and convergence to the physically relevant solutions such as schemes especially deviced for treating shoclcs, contact discontinuities and artificial boundaries. Twenty four papers contain multidimensional computational applications to nonlinear waves in solids, flow through porous media and compressible fluid flow including shoclcs, real gas effects, multiphase phenomena, chemical reactions etc. The editors and organizers of the Second International Conference on Hyperbolic Problems would lilce to thanlc the Scientific Committee for the generous support of recommending invited lectures and selecting the contributed papers of the conference.

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 : 52,5 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.