Large Time Behavior Of Solutions For General Quasi Linear Hyperbolic Parabolic Systems Of Conservation Laws Volume 125 Number 599
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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.
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 Quasilinear Hyperbolic Parabolic Systems Of Conservation Laws
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Author : Tai-Ping Liu
language : en
Publisher:
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 this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Conservation laws categories.
Shock Waves In Conservation Laws With Physical Viscosity
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Author : Tai-Ping Liu
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-02-06
Shock Waves In Conservation Laws With Physical Viscosity 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 2015-02-06 with Mathematics categories.
The authors study the perturbation of a shock wave in conservation laws with physical viscosity. They obtain the detailed pointwise estimates of the solutions. In particular, they show that the solution converges to a translated shock profile. The strength of the perturbation and that of the shock are assumed to be small but independent. The authors' assumptions on the viscosity matrix are general so that their results apply to the Navier-Stokes equations for the compressible fluid and the full system of magnetohydrodynamics, including the cases of multiple eigenvalues in the transversal fields, as long as the shock is classical. The authors' analysis depends on accurate construction of an approximate Green's function. The form of the ansatz for the perturbation is carefully constructed and is sufficiently tight so that the author can close the nonlinear term through Duhamel's principle.
Hyperbolic Problems Theory Numerics And Applications In 2 Volumes
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Author : Tatsien Li
language : en
Publisher: World Scientific
Release Date : 2012-09-28
Hyperbolic Problems Theory Numerics And Applications In 2 Volumes written by Tatsien Li and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-28 with Mathematics categories.
This two-volume book is devoted to mathematical theory, numerics and applications of hyperbolic problems. Hyperbolic problems have not only a long history but also extremely rich physical background. The development is highly stimulated by their applications to Physics, Biology, and Engineering Sciences; in particular, by the design of effective numerical algorithms. Due to recent rapid development of computers, more and more scientists use hyperbolic partial differential equations and related evolutionary equations as basic tools when proposing new mathematical models of various phenomena and related numerical algorithms.This book contains 80 original research and review papers which are written by leading researchers and promising young scientists, which cover a diverse range of multi-disciplinary topics addressing theoretical, modeling and computational issues arising under the umbrella of ';Hyperbolic Partial Differential Equations';. It is aimed at mathematicians, researchers in applied sciences and graduate students.
Navier Stokes Equations
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Author : Roger Temam
language : en
Publisher: American Mathematical Society
Release Date : 2024-05-24
Navier Stokes Equations written by Roger Temam and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-24 with Mathematics categories.
Originally published in 1977, the book is devoted to the theory and numerical analysis of the Navier-Stokes equations for viscous incompressible fluid. On the theoretical side, results related to the existence, the uniqueness, and, in some cases, the regularity of solutions are presented. On the numerical side, various approaches to the approximation of Navier-Stokes problems by discretization are considered, such as the finite dereference method, the finite element method, and the fractional steps method. The problems of stability and convergence for numerical methods are treated as completely as possible. The new material in the present book (as compared to the preceding 1984 edition) is an appendix reproducing a survey article written in 1998. This appendix touches upon a few aspects not addressed in the earlier editions, in particular a short derivation of the Navier-Stokes equations from the basic conservation principles in continuum mechanics, further historical perspectives, and indications on new developments in the area. The appendix also surveys some aspects of the related Euler equations and the compressible Navier-Stokes equations. The book is written in the style of a textbook and the author has attempted to make the treatment self-contained. It can be used as a textbook or a reference book for researchers. Prerequisites for reading the book include some familiarity with the Navier-Stokes equations and some knowledge of functional analysis and Sololev spaces.
Vanishing Viscosity Method
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Author : Boling Guo
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-01-01
Vanishing Viscosity Method written by Boling Guo and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-01 with Mathematics categories.
The book summarizes several mathematical aspects of the vanishing viscosity method and considers its applications in studying dynamical systems such as dissipative systems, hyperbolic conversion systems and nonlinear dispersion systems. Including original research results, the book demonstrates how to use such methods to solve PDEs and is an essential reference for mathematicians, physicists and engineers working in nonlinear science. Contents: Preface Sobolev Space and Preliminaries The Vanishing Viscosity Method of Some Nonlinear Evolution System The Vanishing Viscosity Method of Quasilinear Hyperbolic System Physical Viscosity and Viscosity of Difference Scheme Convergence of Lax–Friedrichs Scheme, Godunov Scheme and Glimm Scheme Electric–Magnetohydrodynamic Equations References
Rendiconti Dell Istituto Di Matematica Dell Universit Di Trieste
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Author : Università degli studi di Trieste. Istituto di matematica
language : en
Publisher:
Release Date : 2000
Rendiconti Dell Istituto Di Matematica Dell Universit Di Trieste written by Università degli studi di Trieste. Istituto di matematica and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
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 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.