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Singular Perturbations I - 1st Edition - ISBN: 9780444881342, 9780080875446

Singular Perturbations I, Volume 23

1st Edition

Spaces and Singular Perturbations on Manifolds Without Boundary

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Author: L.S. Frank
eBook ISBN: 9780080875446
Imprint: North Holland
Published Date: 16th August 1990
Page Count: 554
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Table of Contents

Manifolds, Functional Analysis, Distributions. Sobolev Spaces of Vectorial Order. Singular Perturbations on Smooth Manifolds without Boundary. Bibliography.


Singular perturbations, one of the central topics in asymptotic analysis, also play a special role in describing physical phenomena such as the propagation of waves in media in the presence of small energy dissipations or dispersions, the appearance of boundary or interior layers in fluid and gas dynamics, as well as in elasticity theory, semi-classical asymptotic approximations in quantum mechanics etc. Elliptic and coercive singular perturbations are of special interest for the asymptotic solution of problems which are characterized by boundary layer phenomena, e.g. the theory of thin buckling plates, elastic rods and beams. This first volume deals with linear singular perturbations (on smooth manifolds without boundary) considered as equicontinuous linear mappings between corresponding families of Sobolev-Slobodetski's type spaces of vectorial order.


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© North Holland 1990
16th August 1990
North Holland
eBook ISBN:


@from:Wei Tao Zhang @qu:This book is divided into three chapters. In Chapter 1, the author introduces basic definitions and results concerning smooth manifolds, classical functional analysis and distributions... In Chapter 2, he discusses the Sobolev spaces H(s) of vectorial order s &egr; R3... The title of Chapter 3 is Singular perturbations on smooth manifolds without boundary... In short, this book incorporates the strong points of singular perturbations, pseudodifferential operators, Sobolev-Slobodetskii type spaces and numerical analysis; it is a very good book. @source:Mathematical Reviews @qu:...contains a lot of interesting examples in many branches of mathematics and applications to important physical phenomena. The presentation is lively and its outstanding feature is its originality; the book is welcome to a large number of specialists. @source:Zentralblatt für Mathematik @qu:Den linearen singulären Störungen und ihren Anwendungsbezügen ist das vorliegende Werk gewidmet... Der systematische Ablauf der folgenden 3 Kapitel des Buches wird an vielen Stellen durch Hinweise, interessante Beispiele und Ausblicke (Notes) am Ende jedes Kapitels aufgelockert... Von den Anwendungsgebieten, auf die entweder hingewiesen wird oder die an Beispielen einbezogen werden, seien u. a. genannt: Aufgaben der Magnetohydrodynamik, des Ladungsträger transports in Halbleitern, der Stabilität von Differenzennäherungen, der linearen Elastizitätstheorie, der Streutheorie sowie der Wahrscheinlichkeitstheorie (Diffusionsprozesse). Ein Literaturverzeichnis mit über 300 Quellenangaben rundet das beeindruckende Werk ab, auf dessen zweiten in Vorbereitung befindlichen Band bereits an mehreren Stellen des Buches hingewiesen wird und den man nach dem Studium des vorliegenden ersten Bandes mit grossem Interesse erwartet. @source:Zeitschrift für Angewandte Mathematik und Mechanik

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About the Author

L.S. Frank