Large Time Behavior Of Solutions For General Quasilinear Hyperbolic Parabolic Systems Of Conservation Laws
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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.
Quasilinear Hyperbolic Systems And Dissipative Mechanisms
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Author : Ling Hsiao
language : en
Publisher: World Scientific
Release Date : 1998-02-24
Quasilinear Hyperbolic Systems And Dissipative Mechanisms written by Ling Hsiao and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-02-24 with Mathematics categories.
This book introduces the recent developments in the subject of quasilinear hyperbolic systems with dissipation, such as frictional damping, relaxation, viscosity and heat diffusion. The mathematical theory behind this subject is emphasized in two ways. One emphasis is based on understanding the influence of the dissipation mechanism on the qualitative behavior of solutions, such as the nonlinear diffusive phenomena caused by damping, and other phenomena (including phase transition) for the case with viscosity and heat diffusion. The second emphasis is to take the systems with the dissipation mechanism as an approach to approximating the corresponding system of quasilinear hyperbolic conservation laws - the zero-limit relaxation, or the zero-limit viscosity, and the related topic of nonlinear stability of waves.
Algebraic Cycles And Hodge Theory
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Author : Mark L. Green
language : en
Publisher: Springer
Release Date : 2004-09-02
Algebraic Cycles And Hodge Theory written by Mark L. Green and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-02 with Mathematics categories.
The main goal of the CIME Summer School on "Algebraic Cycles and Hodge Theory" has been to gather the most active mathematicians in this area to make the point on the present state of the art. Thus the papers included in the proceedings are surveys and notes on the most important topics of this area of research. They include infinitesimal methods in Hodge theory; algebraic cycles and algebraic aspects of cohomology and k-theory, transcendental methods in the study of algebraic cycles.
Hyperbolic Problems Theory Numerics Applications Proceedings Of The Fifth International Conference
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Author : James Glimm
language : en
Publisher: World Scientific
Release Date : 1996-03-14
Hyperbolic Problems Theory Numerics Applications Proceedings Of The Fifth International Conference written by James Glimm and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-03-14 with categories.
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.
Hyperbolic Systems Of Balance Laws
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Author : Alberto Bressan
language : en
Publisher: Springer
Release Date : 2007-05-26
Hyperbolic Systems Of Balance Laws written by Alberto Bressan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-26 with Mathematics categories.
This volume includes four lecture courses by Bressan, Serre, Zumbrun and Williams and a Tutorial by Bressan on the Center Manifold Theorem. Bressan introduces the vanishing viscosity approach and clearly explains the building blocks of the theory. Serre focuses on existence and stability for discrete shock profiles. The lectures by Williams and Zumbrun deal with the stability of multidimensional fronts.
Hyperbolic Problems Theory Numerics Applications
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Author : Sylvie Benzoni-Gavage
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-12
Hyperbolic Problems Theory Numerics Applications written by Sylvie Benzoni-Gavage 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 2008-01-12 with Mathematics categories.
This volume contains papers that were presented at HYP2006, the eleventh international Conference on Hyperbolic Problems: Theory, Numerics and Applications. This biennial series of conferences has become one of the most important international events in Applied Mathematics. As computers became more and more powerful, the interplay between theory, modeling, and numerical algorithms gained considerable impact, and the scope of HYP conferences expanded accordingly.
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
Hyperbolic Problems Theory Numerics Applications
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Author : Thomas Y. Hou
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Hyperbolic Problems Theory Numerics Applications written by Thomas Y. Hou 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 2012-12-06 with Mathematics categories.
The International Conference on "Hyperbolic Problems: Theory, Numerics and Applications'' was held in CalTech on March 25-30, 2002. The conference was the ninth meeting in the bi-annual international series which became one of the highest quality and most successful conference series in Applied mathematics. This volume contains more than 90 contributions presented in this conference, including plenary presentations by A. Bressan, P. Degond, R. LeVeque, T.-P. Liu, B. Perthame, C.-W. Shu, B. Sjögreen and S. Ukai. Reflecting the objective of series, the contributions in this volume keep the traditional blend of theory, numerics and applications. The Hyp2002 meeting placed a particular emphasize on fundamental theory and numerical analysis, on multi-scale analysis, modeling and simulations, and on geophysical applications and free boundary problems arising from materials science and multi-component fluid dynamics. The volume should appeal to researchers, students and practitioners with general interest in time-dependent problems governed by hyperbolic equations.
Hyperbolic Problems
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Author : Song Jiang
language : en
Publisher: World Scientific
Release Date : 2012
Hyperbolic Problems written by Song Jiang 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 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 OC Hyperbolic Partial Differential EquationsOCO. It is aimed at mathematicians, researchers in applied sciences and graduate students."