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Author : C. M. Brauner,B. Gay,J. Mathieu
Publisher : Unknown
Page : 552 pages
File Size : 40,5 Mb
Release : 2014-09-01
Category : Electronic
ISBN : 3662180723
Author : C.M. Brauner,B. Gay,J. Mathieu
Publisher : Springer
Page : 551 pages
File Size : 40,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540373407
Author : Paco Lagerstrom
Publisher : Elsevier
Page : 384 pages
File Size : 40,6 Mb
Release : 2012-12-02
Category : Science
ISBN : 9780323152822
Fluid Mechanics and Singular Perturbations: A Collection of Papers by Saul Kaplun focuses on the works and contributions of Saul Kaplun to the studies of fluid mechanics and singular perturbations. The book first discusses the role of coordinate system in boundary-layer theory. Boundary-layer approximations as limits of exact solutions; comparison of different boundary-layer solutions; and comparison with exact solution and choice of optimal are discussed. The text also looks at asymptotic experiment of Navier-Stokes solution for small Reynolds numbers; basic concepts in the theory of singular perturbations and their applications to flow at small Reynolds numbers; and low Reynolds number flow. The book discusses as well a generalization of Poiseuille and Couette flows and nature of solutions of the boundary-layer equations. Numerical solutions and analyses are presented. The text also looks at compatibility condition for boundary layer equation at a point of zero skin friction. Intuitive background; the past-like solution and its principal asymptotic expansions; and class of compatible profiles are discussed. The book is a valuable source of information for readers who want to study fluid mechanics.
Author : Gung-Min Gie,Makram Hamouda,Chang-Yeol Jung,Roger M. Temam
Publisher : Springer
Page : 412 pages
File Size : 49,9 Mb
Release : 2018-11-21
Category : Mathematics
ISBN : 9783030006389
Singular perturbations occur when a small coefficient affects the highest order derivatives in a system of partial differential equations. From the physical point of view singular perturbations generate in the system under consideration thin layers located often but not always at the boundary of the domains that are called boundary layers or internal layers if the layer is located inside the domain. Important physical phenomena occur in boundary layers. The most common boundary layers appear in fluid mechanics, e.g., the flow of air around an airfoil or a whole airplane, or the flow of air around a car. Also in many instances in geophysical fluid mechanics, like the interface of air and earth, or air and ocean. This self-contained monograph is devoted to the study of certain classes of singular perturbation problems mostly related to thermic, fluid mechanics and optics and where mostly elliptic or parabolic equations in a bounded domain are considered. This book is a fairly unique resource regarding the rigorous mathematical treatment of boundary layer problems. The explicit methodology developed in this book extends in many different directions the concept of correctors initially introduced by J. L. Lions, and in particular the lower- and higher-order error estimates of asymptotic expansions are obtained in the setting of functional analysis. The review of differential geometry and treatment of boundary layers in a curved domain is an additional strength of this book. In the context of fluid mechanics, the outstanding open problem of the vanishing viscosity limit of the Navier-Stokes equations is investigated in this book and solved for a number of particular, but physically relevant cases. This book will serve as a unique resource for those studying singular perturbations and boundary layer problems at the advanced graduate level in mathematics or applied mathematics and may be useful for practitioners in other related fields in science and engineering such as aerodynamics, fluid mechanics, geophysical fluid mechanics, acoustics and optics.
Author : E.M. de Jager,J.F. Furu
Publisher : Elsevier
Page : 339 pages
File Size : 43,9 Mb
Release : 1996-11-08
Category : Mathematics
ISBN : 0080542751
The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathematical justification of these methods. The latter implies a priori estimates of solutions of differential equations; this involves the application of Gronwall's lemma, maximum principles, energy integrals, fixed point theorems and Gåding's theorem for general elliptic equations. These features make the book of value to mathematicians and researchers in the engineering sciences, interested in the mathematical justification of formal approximations of solutions of practical perturbation problems. The text is selfcontained and each chapter is concluded with some exercises.
Author : Ferdinand Verhulst
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 48,7 Mb
Release : 2006-06-04
Category : Mathematics
ISBN : 9780387283135
Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach
Author : Symposium on Singular Perturbations and Boundary Layer Theory (Lyon))
Publisher : Unknown
Page : 539 pages
File Size : 40,9 Mb
Release : 1977
Category : Electronic
ISBN : OCLC:658164524
Author : Frederick A. Howes
Publisher : American Mathematical Soc.
Page : 116 pages
File Size : 45,8 Mb
Release : 1978
Category : Boundary value problems
ISBN : 9780821822036
For three classes of singularly perturbed boundary value problems we study the existence of solutions which possess boundary, shock and corner layer behavior and we examine how these nonuniformities arise and how they influence one another. The keys to our analysis are the stability properties of solutions of corresponding reduced problems and the geometric properties of solutions of the boundary value problems inside such layers. Several examples of the theory are discussed in detail with a view to illustrating the naturalness of our approach.
Author : C. M. Brauner,B. Gay,Jean Mathieu
Publisher : Unknown
Page : 540 pages
File Size : 50,5 Mb
Release : 1977
Category : Electronic
ISBN : OCLC:859808691
Author : W. Eckhaus,E.M. de Jager
Publisher : Springer
Page : 371 pages
File Size : 40,5 Mb
Release : 2007-01-05
Category : Mathematics
ISBN : 9783540393320
Author : Robert E. Jr. O'Malley
Publisher : Elsevier
Page : 215 pages
File Size : 52,7 Mb
Release : 2012-12-02
Category : Mathematics
ISBN : 9780323162272
Introduction to Singular Perturbations provides an overview of the fundamental techniques for obtaining asymptomatic solutions to boundary value problems. This text explores singular perturbation techniques, which are among the basic tools of several applied scientists. This book is organized into eight chapters, wherein Chapter 1 discusses the method of matched asymptomatic expansions, which has been frequently applied to several physical problems involving singular perturbations. Chapter 2 considers the nonlinear initial value problem to illustrate the regular perturbation method, and Chapter 3 explains how to construct asymptotic solutions for general linear equations. Chapter 4 discusses scalar equations and nonlinear system, whereas Chapters 5 and 6 explain the contrasts for initial value problems where the outer expansion cannot be determined without obtaining the initial values of the boundary layer correction. Chapters 7 and 8 deal with boundary value problem that arises in the study of adiabatic tubular chemical flow reactors with axial diffusion. This monograph is a valuable resource for applied mathematicians, engineers, researchers, students, and readers whose interests span a variety of fields.
Author : Desineni S. Naidu
Publisher : IET
Page : 314 pages
File Size : 53,7 Mb
Release : 1988
Category : Technology & Engineering
ISBN : 086341107X
This book presents the twin topics of singular perturbation methods and time scale analysis to problems in systems and control. The heart of the book is the singularly perturbed optimal control systems, which are notorious for demanding excessive computational costs. The book addresses both continuous control systems (described by differential equations) and discrete control systems (characterised by difference equations).
Author : Luminita Barbu,Gheorghe Morosanu
Publisher : Springer Science & Business Media
Page : 231 pages
File Size : 43,7 Mb
Release : 2007-12-14
Category : Mathematics
ISBN : 9783764383312
This book offers a detailed asymptotic analysis of some important classes of singularly perturbed boundary value problems which are mathematical models for phenomena in biology, chemistry, and engineering. The authors are particularly interested in nonlinear problems, which have gone little-examined so far in literature dedicated to singular perturbations. The treatment presented here combines successful results from functional analysis, singular perturbation theory, partial differential equations, and evolution equations.
Author : S. A. Lomov
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 45,5 Mb
Release : 2024-07-03
Category : Mathematics
ISBN : 0821897411
This book is aimed at researchers and students in physics, mathematics, and engineering. It contains the first systematic presentation of a general approach to the integration of singularly perturbed differential equations describing nonuniform transitions, such as the occurrence of a boundary layer, discontinuities, boundary effects and so on. The method of regularization of singular perturbations presented here can be applied to the asymptotic integration of systems of ordinary and partial differential equations.
Author : Herrmann Schlichting,Klaus Gersten
Publisher : Springer Science & Business Media
Page : 840 pages
File Size : 48,8 Mb
Release : 2003-05-20
Category : Technology & Engineering
ISBN : 3540662707
A new edition of the almost legendary textbook by Schlichting completely revised by Klaus Gersten is now available. This book presents a comprehensive overview of boundary-layer theory and its application to all areas of fluid mechanics, with emphasis on the flow past bodies (e.g. aircraft aerodynamics). It contains the latest knowledge of the subject based on a thorough review of the literature over the past 15 years. Yet again, it will be an indispensable source of inexhaustible information for students of fluid mechanics and engineers alike.