Admissibility Criteria for Hyperbolic Conservation Laws with Applications to Nonlinear Elasticity PDF Download

Author: Reza Malek-Madani
Publisher:
ISBN:
Category :
Languages : en
Pages : 98

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Author: Barbara Lee Keyfitz
Publisher: American Mathematical Soc.
ISBN: 0821850695
Category : Mathematics
Languages : en
Pages : 148

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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: Tai-Ping Liu
Publisher: American Mathematical Soc.
ISBN: 0821822403
Category : Conservation laws
Languages : en
Pages : 86

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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: C. M. Dafermos
Publisher: 清华大学出版社有限公司
ISBN: 9787302102038
Category : Conservation laws (Physics)
Languages : en
Pages : 466

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Author: Constantine M. Dafermos
Publisher: Springer Science & Business Media
ISBN: 3540290893
Category : Mathematics
Languages : en
Pages : 636

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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: Tai-Ping Liu
Publisher: SIAM
ISBN: 0898714362
Category : Mathematics
Languages : en
Pages : 78

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An in-depth analysis of wave interactions for general systems of hyperbolic and viscous conservation laws.

Author: Josef Ballmann
Publisher: Springer Science & Business Media
ISBN: 3322878694
Category : Technology & Engineering
Languages : en
Pages : 729

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Book Description
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.

Author: Philippe G. LeFloch
Publisher: Springer Science & Business Media
ISBN: 9783764366872
Category : Mathematics
Languages : en
Pages : 1010

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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: Heinrich Freistühler
Publisher: Birkhäuser
ISBN: 3034883722
Category : Mathematics
Languages : en
Pages : 471

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Book Description
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.

Author: Stuart Antman
Publisher: Springer Science & Business Media
ISBN: 0387276491
Category : Mathematics
Languages : en
Pages : 845

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Book Description
Enlarged, updated, and extensively revised, this second edition illuminates specific problems of nonlinear elasticity, emphasizing the role of nonlinear material response. Opening chapters discuss strings, rods, and shells, and applications of bifurcation theory and the calculus of variations to problems for these bodies. Subsequent chapters cover tensors, three-dimensional continuum mechanics, three-dimensional elasticity , general theories of rods and shells, and dynamical problems. Each chapter includes interesting, challenging, and tractable exercises.