Large Time Behavior Of Periodic Solutions Of Hyperbolic Systems Of Conservation Laws
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Large Time Behavior Of Periodic Solutions Of Hyperbolic Systems Of Conservation Laws
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Author : Constantine M. Dafermos
language : en
Publisher:
Release Date : 1994
Large Time Behavior Of Periodic Solutions Of Hyperbolic Systems Of Conservation Laws written by Constantine M. Dafermos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Conservation laws (Physics) categories.
Admissible Solutions Of Hyperbolic Conservation Laws
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Author : Tai-Ping Liu
language : en
Publisher: American Mathematical Soc.
Release Date : 1981
Admissible Solutions Of Hyperbolic Conservation Laws written by Tai-Ping Liu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Conservation laws categories.
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.
Hyperbolic Systems Of Conservation Laws And The Mathematical Theory Of Shock Waves
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Author : Peter D. Lax
language : en
Publisher: SIAM
Release Date : 1973-01-01
Hyperbolic Systems Of Conservation Laws And The Mathematical Theory Of Shock Waves written by Peter D. Lax and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973-01-01 with Technology & Engineering categories.
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.
Large Time Behavior Of Solutions For General Quasilinear Hyperbolic Parabolic Systems Of Conservation Laws
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Author : Tai-Ping Liu
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Large Time Behavior Of Solutions For General Quasilinear Hyperbolic Parabolic Systems Of Conservation Laws written by Tai-Ping Liu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
We are interested in the time-asymptotic behavior of solutions to viscous conservation laws. Through the pointwise estimates for the Green's function of the linearized system and the analysis of coupling of nonlinear diffusion waves, we obtain explicit expressions of the time-asymptotic behavior of the solutions. This yields optimal estimates in the integral norms. For most physical models, the viscosity matrix is not positive definite and the system is hyperbolic-parabolic, and not uniformly parabolic. This implies that the Green's function may contain Dirac [lowercase Greek]Delta-functions. When the corresponding inviscid system is non-strictly hyperbolic, the time-asymptotic state contains generalized Burgers solutions. These are illustrated by applying our general theory to the compressible Navier-Stokes equations and the equations of magnetohydrodynamics.
Large Time Behavior Of Solutions For General Quasi Linear Hyperbolic Parabolic Systems Of Conservation Laws Volume 125 Number 599
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Author :
language : en
Publisher:
Release Date : 1997
Large Time Behavior Of Solutions For General Quasi Linear Hyperbolic Parabolic Systems Of Conservation Laws Volume 125 Number 599 written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
We are interested in the time-asymptotic behavior of solutions to viscous conservation laws. Through the pointwise estimates for the Green's function of the linearized system and the analysis of coupling of nonlinear diffusion waves, we obtain explicit expressions of the time-asymptotic behavior of the solutions. This yields optimal estimates in the integral norms. For most physical models, the viscosity matrix is not positive definite and the system is hyperbolic-parabolic, and not uniformly parabolic. This implies that the Green's function may contain Dirac-functions. When the corresponding inviscid system is non-strictly hyperbolic, the time-asymptotic state contains generalized Burgers solutions. These are illustrated by applying our general theory to the compressible Navier-Stokes equations and the equations of magnetohydrodynamics.
Hyperbolic Systems Of Conservation Laws
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Author : Philippe G. LeFloch
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-07-01
Hyperbolic Systems Of Conservation Laws written by Philippe G. LeFloch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-01 with Mathematics categories.
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.
Analysis Of Systems Of Conservation Laws
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Author : Heinrich Freistuhler
language : en
Publisher: CRC Press
Release Date : 1998-12-30
Analysis Of Systems Of Conservation Laws written by Heinrich Freistuhler and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-30 with Mathematics categories.
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
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Author : Constantine M. Dafermos
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-16
Hyperbolic Conservation Laws In Continuum Physics written by Constantine M. Dafermos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-16 with Mathematics categories.
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
Numerical Methods For Conservation Laws
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Author : Randall J. LeVeque
language : en
Publisher: Springer Science & Business Media
Release Date : 1992
Numerical Methods For Conservation Laws written by Randall J. LeVeque and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
These notes were developed for a graduate-level course on the theory and numerical solution of nonlinear hyperbolic systems of conservation laws. Part I deals with the basic mathematical theory of the equations: the notion of weak solutions, entropy conditions, and a detailed description of the wave structure of solutions to the Riemann problem. The emphasis is on tools and techniques that are indispensable in developing good numerical methods for discontinuous solutions. Part II is devoted to the development of high resolution shock-capturing methods, including the theory of total variation diminishing (TVD) methods and the use of limiter functions. The book is intended for a wide audience, and will be of use both to numerical analysts and to computational researchers in a variety of applications.
Hyperbolic Conservation Laws In Continuum Physics
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Author : Constantine M. Dafermos
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Hyperbolic Conservation Laws In Continuum Physics written by Constantine M. Dafermos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
This masterly exposition of the mathematical theory of hyperbolic system laws brings out the intimate connection with continuum thermodynamics, emphasizing issues in which the analysis may reveal something about the physics and, in return, the underlying physical structure may direct and drive the analysis.