The Asymptotic Decay of Shock Waves PDF Download

Author: A. Coombs
Publisher:
ISBN:
Category :
Languages : en
Pages : 49

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Author: Subrahmanyan Chandrasekhar
Publisher:
ISBN:
Category : Shock waves
Languages : en
Pages : 38

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Author: Heinrich Freistühler
Publisher: Springer Science & Business Media
ISBN: 1461201934
Category : Mathematics
Languages : en
Pages : 527

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Book Description
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.

Author: Kurt Otto Friedrichs
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Author: Tai-Ping Liu
Publisher: American Mathematical Soc.
ISBN: 1470466252
Category : Education
Languages : en
Pages : 437

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Book Description
This book presents the fundamentals of the shock wave theory. The first part of the book, Chapters 1 through 5, covers the basic elements of the shock wave theory by analyzing the scalar conservation laws. The main focus of the analysis is on the explicit solution behavior. This first part of the book requires only a course in multi-variable calculus, and can be used as a text for an undergraduate topics course. In the second part of the book, Chapters 6 through 9, this general theory is used to study systems of hyperbolic conservation laws. This is a most significant well-posedness theory for weak solutions of quasilinear evolutionary partial differential equations. The final part of the book, Chapters 10 through 14, returns to the original subject of the shock wave theory by focusing on specific physical models. Potentially interesting questions and research directions are also raised in these chapters. The book can serve as an introductory text for advanced undergraduate students and for graduate students in mathematics, engineering, and physical sciences. Each chapter ends with suggestions for further reading and exercises for students.

Author: Kurt Otto Friedrichs
Publisher: Forgotten Books
ISBN: 9781334256905
Category :
Languages : en
Pages : 36

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Book Description
Excerpt from Formation and Decay of Shock Waves Apart from its theoretical interest the method leads to simple procedures for numerical calculation. In the appendices of a more detailed publication the mathematical theory will be amplified, further applications, especially to the theory of water waves in shallow channels will be presented, and the accuracy of the approximate results will be demonstrated. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Author: Peter D. Lax
Publisher: SIAM
ISBN: 0898711770
Category : Technology & Engineering
Languages : en
Pages : 55

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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.

Author: Robert V. Hess
Publisher:
ISBN:
Category : Gas dynamics
Languages : en
Pages : 72

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Book Description
This paper treats the interaction between hot layers extended along the wall and normal or oblique shocks moving over them. Emphasis is on the cases of large hot-layer temperatures and strong shock waves for which small-perturbation theories are not applicable. A variety of possible interaction patterns are described. Of greatest interest are the more extreme cases when the hot layer is forced to accumulate in a growing bubble-like region bound to the moving shock, and some of the cold air above the layer moves around the bubble and interposes a high-speed forward-moving cold jet between the wall and the bubble. For some cases, especially with oblique shocks, this reverse jet may not form. Mixing will eventually limit the size of the bubble and make its characteristics more nearly like those of the more familiar separation bubbles. The effects of viscosity at the wall remains essentially different, however, since the shock is moving relative to the wall.

Author: Joel Smoller
Publisher: Springer Science & Business Media
ISBN: 1461208734
Category : Mathematics
Languages : en
Pages : 650

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Book Description
For this edition, a number of typographical errors and minor slip-ups have been corrected. In addition, following the persistent encouragement of Olga Oleinik, I have added a new chapter, Chapter 25, which I titled "Recent Results." This chapter is divided into four sections, and in these I have discussed what I consider to be some of the important developments which have come about since the writing of the first edition. Section I deals with reaction-diffusion equations, and in it are described both the work of C. Jones, on the stability of the travelling wave for the Fitz-Hugh-Nagumo equations, and symmetry-breaking bifurcations. Section II deals with some recent results in shock-wave theory. The main topics considered are L. Tartar's notion of compensated compactness, together with its application to pairs of conservation laws, and T.-P. Liu's work on the stability of viscous profiles for shock waves. In the next section, Conley's connection index and connection matrix are described; these general notions are useful in con structing travelling waves for systems of nonlinear equations. The final sec tion, Section IV, is devoted to the very recent results of C. Jones and R. Gardner, whereby they construct a general theory enabling them to locate the point spectrum of a wide class of linear operators which arise in stability problems for travelling waves. Their theory is general enough to be applica ble to many interesting reaction-diffusion systems.

Author: Gabi Ben-Dor
Publisher: Elsevier
ISBN: 0080533728
Category : Science
Languages : en
Pages : 2188

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Book Description
The Handbook of Shock Waves contains a comprehensive, structured coverage of research topics related to shock wave phenomena including shock waves in gases, liquids, solids, and space. Shock waves represent an extremely important physical phenomena which appears to be of special practical importance in three major fields: compressible flow (aerodynamics), materials science, and astrophysics. Shock waves comprise a phenomenon that occurs when pressure builds to force a reaction, i.e. sonic boom that occurs when a jet breaks the speed of sound.This Handbook contains experimental, theoretical, and numerical results which never before appeared under one cover; the first handbook of its kind.The Handbook of Shock Waves is intended for researchers and engineers active in shock wave related fields. Additionally, R&D establishments, applied science & research laboratories and scientific and engineering libraries both in universities and government institutions. As well as, undergraduate and graduate students in fluid mechanics, gas dynamics, and physics. Key Features* Ben-Dor is known as one of the founders of the field of shock waves* Covers a broad spectrum of shock wave research topics* Provides a comprehensive description of various shock wave related subjects* First handbook ever to include under one separate cover: experimental, theoretical, and numerical results