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

Tai-Ping Liu,Yanni Zeng
Large Time Behavior of Solutions for General Quasilinear Hyperbolic Parabolic Systems of Conservation Laws Book PDF

Author : Tai-Ping Liu,Yanni Zeng
Publisher : American Mathematical Soc.
Page : 135 pages
File Size : 41,6 Mb
Release : 1997
Category : Conservation laws
ISBN : 9780821805459

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Large Time Behavior of Solutions for General Quasilinear Hyperbolic-Parabolic Systems of Conservation Laws by Tai-Ping Liu,Yanni Zeng Pdf

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.

Theory, Numerics and Applications of Hyperbolic Problems I

Christian Klingenberg,Michael Westdickenberg
Theory Numerics and Applications of Hyperbolic Problems I Book PDF

Author : Christian Klingenberg,Michael Westdickenberg
Publisher : Springer
Page : 706 pages
File Size : 43,5 Mb
Release : 2018-06-23
Category : Mathematics
ISBN : 9783319915456

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Theory, Numerics and Applications of Hyperbolic Problems I by Christian Klingenberg,Michael Westdickenberg Pdf

The first of two volumes, this edited proceedings book features research presented at the XVI International Conference on Hyperbolic Problems held in Aachen, Germany in summer 2016. It focuses on the theoretical, applied, and computational aspects of hyperbolic partial differential equations (systems of hyperbolic conservation laws, wave equations, etc.) and of related mathematical models (PDEs of mixed type, kinetic equations, nonlocal or/and discrete models) found in the field of applied sciences.

Algebraic Cycles and Hodge Theory

Mark L. Green,Jacob P. Murre,Claire Voisin
Algebraic Cycles and Hodge Theory Book PDF

Author : Mark L. Green,Jacob P. Murre,Claire Voisin
Publisher : Springer
Page : 276 pages
File Size : 40,9 Mb
Release : 2004-09-03
Category : Mathematics
ISBN : 9783540490463

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Algebraic Cycles and Hodge Theory by Mark L. Green,Jacob P. Murre,Claire Voisin Pdf

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.

Vanishing Viscosity Method

Boling Guo,Dongfen Bian,Fangfang Li,Xiaoyu Xi
Vanishing Viscosity Method Book PDF

Author : Boling Guo,Dongfen Bian,Fangfang Li,Xiaoyu Xi
Publisher : Walter de Gruyter GmbH & Co KG
Page : 569 pages
File Size : 44,7 Mb
Release : 2017-01-01
Category : Mathematics
ISBN : 9783110494273

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Vanishing Viscosity Method by Boling Guo,Dongfen Bian,Fangfang Li,Xiaoyu Xi Pdf

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

Thomas Y. Hou,Eitan Tadmor
Hyperbolic Problems Theory Numerics Applications Book PDF

Author : Thomas Y. Hou,Eitan Tadmor
Publisher : Springer Science & Business Media
Page : 946 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642557118

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Hyperbolic Problems: Theory, Numerics, Applications by Thomas Y. Hou,Eitan Tadmor Pdf

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.

Analysis of Systems of Conservation Laws

Heinrich Freistuhler
Analysis of Systems of Conservation Laws Book PDF

Author : Heinrich Freistuhler
Publisher : CRC Press
Page : 276 pages
File Size : 41,5 Mb
Release : 1998-12-30
Category : Mathematics
ISBN : 0849306442

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Analysis of Systems of Conservation Laws by Heinrich Freistuhler Pdf

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 Problems: Contributed talks

Eitan Tadmor,Jian-Guo Liu,Athanasios E. Tzavaras
Hyperbolic Problems Contributed talks Book PDF

Author : Eitan Tadmor,Jian-Guo Liu,Athanasios E. Tzavaras
Publisher : American Mathematical Soc.
Page : 690 pages
File Size : 55,9 Mb
Release : 2009-12-15
Category : Mathematics
ISBN : 9780821847305

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Hyperbolic Problems: Contributed talks by Eitan Tadmor,Jian-Guo Liu,Athanasios E. Tzavaras Pdf

The International Conference on Hyperbolic Problems: Theory, Numerics and Applications, ``HYP2008'', was held at the University of Maryland from June 9-13, 2008. This was the twelfth meeting in the bi-annual international series of HYP conferences which originated in 1986 at Saint-Etienne, France, and over the last twenty years has become one of the highest quality and most successful conference series in Applied Mathematics. This book, the second in a two-part volume, contains more than sixty articles based on contributed talks given at the conference. The articles are written by leading researchers as well as promising young scientists and cover a diverse range of multi-disciplinary topics addressing theoretical, modeling and computational issues arising under the umbrella of ``hyperbolic PDEs''. This volume will bring readers to the forefront of research in this most active and important area in applied mathematics.

Handbook of Mathematical Fluid Dynamics

S. Friedlander,D. Serre
Handbook of Mathematical Fluid Dynamics Book PDF

Author : S. Friedlander,D. Serre
Publisher : Elsevier
Page : 702 pages
File Size : 48,9 Mb
Release : 2004-11-20
Category : Mathematics
ISBN : 0444515569

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Handbook of Mathematical Fluid Dynamics by S. Friedlander,D. Serre Pdf

The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.

Hyperbolic Systems of Balance Laws

Alberto Bressan,Denis Serre,Mark Williams,Kevin Zumbrun
Hyperbolic Systems of Balance Laws Book PDF

Author : Alberto Bressan,Denis Serre,Mark Williams,Kevin Zumbrun
Publisher : Springer
Page : 365 pages
File Size : 40,8 Mb
Release : 2007-05-26
Category : Mathematics
ISBN : 9783540721871

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Hyperbolic Systems of Balance Laws by Alberto Bressan,Denis Serre,Mark Williams,Kevin Zumbrun Pdf

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.

Shock Waves in Conservation Laws with Physical Viscosity

Tai-Ping Liu,Yanni Zeng
Shock Waves in Conservation Laws with Physical Viscosity Book PDF

Author : Tai-Ping Liu,Yanni Zeng
Publisher : American Mathematical Soc.
Page : 168 pages
File Size : 49,8 Mb
Release : 2015-02-06
Category : Conservation laws (Mathematics)
ISBN : 9781470410162

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Shock Waves in Conservation Laws with Physical Viscosity by Tai-Ping Liu,Yanni Zeng Pdf

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.

Nonlinear Problems of Elasticity

Stuart Antman
Nonlinear Problems of Elasticity Book PDF

Author : Stuart Antman
Publisher : Springer Science & Business Media
Page : 845 pages
File Size : 41,7 Mb
Release : 2005-11-24
Category : Mathematics
ISBN : 9780387276496

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Nonlinear Problems of Elasticity by Stuart Antman Pdf

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.

Advances in the Theory of Shock Waves

Heinrich Freistühler,Anders Szepessy
Advances in the Theory of Shock Waves Book PDF

Author : Heinrich Freistühler,Anders Szepessy
Publisher : Springer Science & Business Media
Page : 527 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201939

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Advances in the Theory of Shock Waves by Heinrich Freistühler,Anders Szepessy Pdf

In the field known as "the mathematical theory of shock waves," very exciting and unexpected developments have occurred in the last few years. Joel Smoller and Blake Temple have established classes of shock wave solutions to the Einstein Euler equations of general relativity; indeed, the mathematical and physical con sequences of these examples constitute a whole new area of research. The stability theory of "viscous" shock waves has received a new, geometric perspective due to the work of Kevin Zumbrun and collaborators, which offers a spectral approach to systems. Due to the intersection of point and essential spectrum, such an ap proach had for a long time seemed out of reach. The stability problem for "in viscid" shock waves has been given a novel, clear and concise treatment by Guy Metivier and coworkers through the use of paradifferential calculus. The L 1 semi group theory for systems of conservation laws, itself still a recent development, has been considerably condensed by the introduction of new distance functionals through Tai-Ping Liu and collaborators; these functionals compare solutions to different data by direct reference to their wave structure. The fundamental prop erties of systems with relaxation have found a systematic description through the papers of Wen-An Yong; for shock waves, this means a first general theorem on the existence of corresponding profiles. The five articles of this book reflect the above developments.

Navier–Stokes Equations

Roger Temam
Navier Stokes Equations Book PDF

Author : Roger Temam
Publisher : American Mathematical Society
Page : 426 pages
File Size : 46,6 Mb
Release : 2024-05-24
Category : Mathematics
ISBN : 9781470477868

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Navier–Stokes Equations by Roger Temam Pdf

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.

Handbook of Differential Equations: Evolutionary Equations

C.M. Dafermos,Eduard Feireisl
Handbook of Differential Equations Evolutionary Equations Book PDF

Author : C.M. Dafermos,Eduard Feireisl
Publisher : Elsevier
Page : 579 pages
File Size : 47,9 Mb
Release : 2004-08-24
Category : Mathematics
ISBN : 9780080521824

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Handbook of Differential Equations: Evolutionary Equations by C.M. Dafermos,Eduard Feireisl Pdf

This book contains several introductory texts concerning the main directions in the theory of evolutionary partial differential equations. The main objective is to present clear, rigorous, and in depth surveys on the most important aspects of the present theory. The table of contents includes: W.Arendt: Semigroups and evolution equations: Calculus, regularity and kernel estimates A.Bressan: The front tracking method for systems of conservation laws E.DiBenedetto, J.M.Urbano,V.Vespri: Current issues on singular and degenerate evolution equations; L.Hsiao, S.Jiang: Nonlinear hyperbolic-parabolic coupled systems A.Lunardi: Nonlinear parabolic equations and systems D.Serre:L1-stability of nonlinear waves in scalar conservation laws B.Perthame:Kinetic formulations of parabolic and hyperbolic PDE’s: from theory to numerics

Hyperbolic Problems: Theory, Numerics, Applications

Sylvie Benzoni-Gavage,Denis Serre
Hyperbolic Problems Theory Numerics Applications Book PDF

Author : Sylvie Benzoni-Gavage,Denis Serre
Publisher : Springer Science & Business Media
Page : 1117 pages
File Size : 51,6 Mb
Release : 2008-01-12
Category : Mathematics
ISBN : 9783540757122

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Hyperbolic Problems: Theory, Numerics, Applications by Sylvie Benzoni-Gavage,Denis Serre Pdf

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.