Download or read book Large Time Behavior of Solutions for General Quasi linear Hyperbolic Parabolic Systems of Conservation Laws Volume 125 Number 599 written by and published by . This book was released on 1997 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Large Time Behavior of Solutions for General Quasilinear Hyperbolic Parabolic Systems of Conservation Laws written by Tai-Ping Liu and published by American Mathematical Soc.. This book was released on 1997 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Large Time Behavior of Solutions for General Quasilinear Hyperbolic parabolic Systems of Conservation Laws written by Tai-Ping Liu and published by . This book was released on 1997 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Shock Waves in Conservation Laws with Physical Viscosity written by Tai-Ping Liu and published by American Mathematical Soc.. This book was released on 2015-02-06 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Vanishing Viscosity Method written by Boling Guo and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-12-05 with total page 716 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Navier Stokes Equations written by Roger Temam and published by American Mathematical Society. This book was released on 2024-05-24 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Rendiconti Dell Istituto Di Matematica Dell Universit Di Trieste written by Università degli studi di Trieste. Istituto di matematica and published by . This book was released on 2000 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Large Time Behavior of Periodic Solutions of Hyperbolic Systems of Conservation Laws written by Constantine M. Dafermos and published by . This book was released on 1994 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book American Book Publishing Record written by and published by . This book was released on 1997-05 with total page 1230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Admissible Solutions of Hyperbolic Conservation Laws written by Tai-Ping Liu and published by American Mathematical Soc.. This book was released on 1981 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Bulletin of the Institute of Mathematics Academia Sinica written by Zhong yang yan jiu yuan. Shu xue yan jiu suo and published by . This book was released on 2006 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book One dimensional Hyperbolic Conservation Laws And Their Applications written by Jean-michel Coron and published by World Scientific. This book was released on 2019-01-08 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of lecture notes for the LIASFMA Shanghai Summer School on 'One-dimensional Hyperbolic Conservation Laws and Their Applications' which was held during August 16 to August 27, 2015 at Shanghai Jiao Tong University, Shanghai, China. This summer school is one of the activities promoted by Sino-French International Associate Laboratory in Applied Mathematics (LIASFMA in short). LIASFMA was established jointly by eight institutions in China and France in 2014, which is aimed at providing a platform for some of the leading French and Chinese mathematicians to conduct in-depth researches, extensive exchanges, and student training in the field of applied mathematics. This summer school has the privilege of being the first summer school of the newly established LIASFMA, which makes it significant.
Download or read book Hyperbolic and Viscous Conservation Laws written by Tai-Ping Liu and published by SIAM. This book was released on 2000-01-01 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: An in-depth analysis of wave interactions for general systems of hyperbolic and viscous conservation laws.
Download or read book Large Time Behavior of Solutions of Hyperbolic Balance Laws written by Constantine M. Dafermos and published by . This book was released on 1984 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Uniform Behavior of Solutions of Linear Hyperbolic Systems for Large Times written by David Goldstein Costa and published by . This book was released on 1973 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On a Hyperbolic System of Conservation Laws Which Is Not Strictly Hyperbolic written by Tai-Ping Liu and published by . This book was released on 1981 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study a system of quasilinear hyperbolic conservation laws which is hyperbolic but not strictly hyperbolic. Such systems arise naturally in continuum mechanics such as elastic, multiphase flows. We are interested mainly in the large time behavior of the solution. Due to the nonlinearity of the system and the entropy condition, solutions converge to very simple elementary waves. Nonstrict hyperbolicity of the system amy cause a stronger nonlinear interactions between waves pertaining to different families; in particular, such interactions may regularize linear waves in the solution. The solutions are constructed using the random choice method. (Author).
Download or read book Development of Mathematics 1950 2000 written by Jean-Paul Pier and published by Springer Science & Business Media. This book was released on 2000-09 with total page 1400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book not only attempts a history of contemporary mathematics, but also provides some authoritative guidance through the maze of mathematical theories. It addresses a range of topics from the personal viewpoint of more than forty mathematicians, most of them active researchers and renowned specialists in their fields.
