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Quasilinear Hyperbolic Systems Compressible Flows And Waves

Author: Vishnu D. Sharma
Publisher: CRC Press
ISBN: 9781439836910
Size: 65.32 MB
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Filled with practical examples, Quasilinear Hyperbolic Systems, Compressible Flows, and Waves presents a self-contained discussion of quasilinear hyperbolic equations and systems with applications. It emphasizes nonlinear theory and introduces some of the most active research in the field. After linking continuum mechanics and quasilinear partial differential equations, the book discusses the scalar conservation laws and hyperbolic systems in two independent variables. Using the method of characteristics and singular surface theory, the author then presents the evolutionary behavior of weak and mild discontinuities in a quasilinear hyperbolic system. He also explains how to apply weakly nonlinear geometrical optics in nonequilibrium and stratified gas flows and demonstrates the power, generality, and elegance of group theoretic methods for solving Euler equations of gasdynamics involving shocks. The final chapter deals with the kinematics of a shock of arbitrary strength in three dimensions. With a focus on physical applications, this text takes readers on a journey through this fascinating area of applied mathematics. It provides the essential mathematical concepts and techniques to understand the phenomena from a theoretical standpoint and to solve a variety of physical problems.

Rational Extended Thermodynamics Beyond The Monatomic Gas

Author: Tommaso Ruggeri
Publisher: Springer
ISBN: 3319133411
Size: 30.19 MB
Format: PDF, Kindle
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This book is dedicated to the recent developments in RET with the aim to explore polyatomic gas, dense gas and mixture of gases in non-equilibrium. In particular we present the theory of dense gases with 14 fields, which reduces to the Navier-Stokes Fourier classical theory in the parabolic limit. Molecular RET with an arbitrary number of field-variables for polyatomic gases is also discussed and the theory is proved to be perfectly compatible with the kinetic theory in which the distribution function depends on an extra variable that takes into account a molecule’s internal degrees of freedom. Recent results on mixtures of gases with multi-temperature are presented together with a natural definition of the average temperature. The qualitative analysis and in particular, the existence of the global smooth solution and the convergence to equilibrium are also studied by taking into account the fact that the differential systems are symmetric hyperbolic. Applications to shock and sound waves are analyzed together with light scattering and heat conduction and the results are compared with experimental data. Rational extended thermodynamics (RET) is a thermodynamic theory that is applicable to non-equilibrium phenomena. It is described by differential hyperbolic systems of balance laws with local constitutive equations. As RET has been strictly related to the kinetic theory through the closure method of moment hierarchy associated to the Boltzmann equation, the applicability range of the theory has been restricted within rarefied monatomic gases. The book represents a valuable resource for applied mathematicians, physicists and engineers, offering powerful models for potential applications like satellites reentering the atmosphere, semiconductors and nano-scale phenomena.

Quasilinear Hyperbolic Systems And Dissipative Mechanisms

Author: L Hsiao
Publisher: World Scientific
ISBN: 9814497185
Size: 71.10 MB
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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. Contents:Frictional Damping: Globally Defined Classical Solutions and Their Nonlinear Diffusive PhenomenaFrictional Damping: Globally Defined Weak Solutions and The Nonlinear Diffusive PhenomenaRelaxationThe Influence of Dissipation Mechanism on the Qualitative Behavior of SolutionsVanishing Viscosity and Nonlinear Stability of Waves Readership: Postgraduate students, mathematicians, physicists and engineers in theoretical and numerical analysis of partial differentiation equations and continuum mechanics. keywords:Problem of Vanishing Viscosity;Relaxation;Dissipation;Large-Time Behaviour;Nonlinear Stability;Zero Relaxation Limit

Hyperbolic Conservation Laws In Continuum Physics

Author: Constantine M. Dafermos
Publisher: Springer Science & Business Media
ISBN: 3540290893
Size: 41.54 MB
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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

Waves And Compressible Flow

Author: Hilary Ockendon
Publisher: Springer Science & Business Media
ISBN: 038740399X
Size: 18.47 MB
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This book covers compressible flow however the authors also show how wave phenomena in electromagnetism and solid mechanics can be treated using similar mathematical methods. It caters to the needs of the modern student by providing the tools necessary for a mathematical analysis of most kinds of waves liable to be encountered in modern science and technology. At the same time emphasis is laid on the physical background and modeling that requires these tools.

Systems Of Quasilinear Equations And Their Applications To Gas Dynamics

Author: Boris Leonidovich Rozhdestvenski_
Publisher: American Mathematical Soc.
ISBN: 9780821898062
Size: 62.18 MB
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This book is essentially a new edition, revised and augmented by results of the last decade, of the work of the same title published in 1968 by ``Nauka.'' It is devoted to mathematical questions of gas dynamics. Topics covered include Foundations of the Theory of Systems of Quasilinear Equations of Hyperbolic Type in Two Independent Variables; Classical and Generalized Solutions of One-Dimensional Gas Dynamics; Difference Methods for Solving the Equations of Gas Dynamics; and Generalized Solutions of Systems of Quasilinear Equations of Hyperbolic Type.