Singular Perturbations And Boundary Layers

Author : Gung-Min Gie,Makram Hamouda,Chang-Yeol Jung,Roger M. Temam
Publisher : Springer
Page : 412 pages
File Size : 46,8 Mb
Release : 2018-11-21
Category : Mathematics
ISBN : 9783030006389

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Singular Perturbations and Boundary Layers by Gung-Min Gie,Makram Hamouda,Chang-Yeol Jung,Roger M. Temam Pdf

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 : C.M. Brauner,B. Gay,J. Mathieu
Publisher : Springer
Page : 551 pages
File Size : 53,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540373407

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Singular Perturbations and Boundary Layer Theory by C.M. Brauner,B. Gay,J. Mathieu Pdf

Author : Ferdinand Verhulst
Publisher : Springer Science & Business Media
Page : 328 pages
File Size : 50,9 Mb
Release : 2006-06-04
Category : Mathematics
ISBN : 9780387283135

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Methods and Applications of Singular Perturbations by Ferdinand Verhulst Pdf

Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach

Author : C. M. Brauner,B. Gay,J. Mathieu
Publisher : Unknown
Page : 552 pages
File Size : 53,5 Mb
Release : 2014-09-01
Category : Electronic
ISBN : 3662180723

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Singular Perturbations and Boundary Layer Theory by C. M. Brauner,B. Gay,J. Mathieu Pdf

Author : Robert E. Jr. O'Malley
Publisher : Elsevier
Page : 214 pages
File Size : 53,9 Mb
Release : 2012-12-02
Category : Mathematics
ISBN : 9780323162272

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Introduction to Singular Perturbations by Robert E. Jr. O'Malley Pdf

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 : Paco Lagerstrom
Publisher : Elsevier
Page : 384 pages
File Size : 48,8 Mb
Release : 2012-12-02
Category : Science
ISBN : 9780323152822

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Fluid Mechanics and Singular Perturbations by Paco Lagerstrom Pdf

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 : E.M. de Jager,J.F. Furu
Publisher : Elsevier
Page : 339 pages
File Size : 49,6 Mb
Release : 1996-11-08
Category : Mathematics
ISBN : 0080542751

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The Theory of Singular Perturbations by E.M. de Jager,J.F. Furu Pdf

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 : Desineni S. Naidu
Publisher : IET
Page : 314 pages
File Size : 43,9 Mb
Release : 1988
Category : Technology & Engineering
ISBN : 086341107X

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Singular Perturbation Methodology in Control Systems by Desineni S. Naidu Pdf

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 : Frederick A. Howes
Publisher : American Mathematical Soc.
Page : 116 pages
File Size : 45,6 Mb
Release : 1978
Category : Boundary value problems
ISBN : 9780821822036

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Boundary-Interior Layer Interactions in Nonlinear Singular Perturbation Theory by Frederick A. Howes Pdf

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 : Adelaida B. Vasil'eva,Valentin F. Butuzov,Leonid V. Kalachev
Publisher : SIAM
Page : 231 pages
File Size : 51,7 Mb
Release : 1995-01-01
Category : Mathematics
ISBN : 9780898713336

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The Boundary Function Method for Singular Perturbed Problems by Adelaida B. Vasil'eva,Valentin F. Butuzov,Leonid V. Kalachev Pdf

This book is devoted solely to the boundary function method, which is one of the asymptotic methods.

Author : Luminita Barbu,Gheorghe Morosanu
Publisher : Springer Science & Business Media
Page : 231 pages
File Size : 54,6 Mb
Release : 2007-12-14
Category : Mathematics
ISBN : 9783764383312

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Singularly Perturbed Boundary-Value Problems by Luminita Barbu,Gheorghe Morosanu Pdf

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 : L.S. Frank
Publisher : Elsevier
Page : 554 pages
File Size : 42,7 Mb
Release : 1990-08-16
Category : Mathematics
ISBN : 0080875440

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Singular Perturbations I by L.S. Frank Pdf

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.

Author : John James Henry Miller,Eugene O'Riordan,G. I. Shishkin
Publisher : World Scientific
Page : 191 pages
File Size : 55,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814390736

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Fitted Numerical Methods for Singular Perturbation Problems by John James Henry Miller,Eugene O'Riordan,G. I. Shishkin Pdf

Since the first edition of this book, the literature on fitted mesh methods for singularly perturbed problems has expanded significantly. Over the intervening years, fitted meshes have been shown to be effective for an extensive set of singularly perturbed partial differential equations. In the revised version of this book, the reader will find an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. The global errors in the numerical approximations are measured in the pointwise maximum norm. The fitted mesh algorithm is particularly simple to implement in practice, but the theory of why these numerical methods work is far from simple. This book can be used as an introductory text to the theory underpinning fitted mesh methods.

Author : W. Eckhaus
Publisher : Elsevier
Page : 286 pages
File Size : 50,8 Mb
Release : 2011-08-30
Category : Mathematics
ISBN : 0080875300

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Asymptotic Analysis of Singular Perturbations by W. Eckhaus Pdf

Asymptotic Analysis of Singular Perturbations

Author : Robert E., Jr. O'Malley
Publisher : Springer Science & Business Media
Page : 234 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209775

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Singular Perturbation Methods for Ordinary Differential Equations by Robert E., Jr. O'Malley Pdf

This book results from various lectures given in recent years. Early drafts were used for several single semester courses on singular perturbation meth ods given at Rensselaer, and a more complete version was used for a one year course at the Technische Universitat Wien. Some portions have been used for short lecture series at Universidad Central de Venezuela, West Vir ginia University, the University of Southern California, the University of California at Davis, East China Normal University, the University of Texas at Arlington, Universita di Padova, and the University of New Hampshire, among other places. As a result, I've obtained lots of valuable feedback from students and listeners, for which I am grateful. This writing continues a pattern. Earlier lectures at Bell Laboratories, at the University of Edin burgh and New York University, and at the Australian National University led to my earlier works (1968, 1974, and 1978). All seem to have been useful for the study of singular perturbations, and I hope the same will be true of this monograph. I've personally learned much from reading and analyzing the works of others, so I would especially encourage readers to treat this book as an introduction to a diverse and exciting literature. The topic coverage selected is personal and reflects my current opin ions. An attempt has been made to encourage a consistent method of ap proaching problems, largely through correcting outer limits in regions of rapid change. Formal proofs of correctness are not emphasized.