Singularly Perturbed Methods For Nonlinear Elliptic Problems

Author : Daomin Cao
Publisher : Cambridge University Press
ISBN 13 : 1108858473
Total Pages : 263 pages
Book Rating : 4.72/5 ( download)

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Download or read book Singularly Perturbed Methods for Nonlinear Elliptic Problems written by Daomin Cao and published by Cambridge University Press. This book was released on 2021-02-18 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to the singularly perturbed methods in the nonlinear elliptic partial differential equations emphasises the existence and local uniqueness of solutions exhibiting concentration property. The authors avoid using sophisticated estimates and explain the main techniques by thoroughly investigating two relatively simple but typical non-compact elliptic problems. Each chapter then progresses to other related problems to help the reader learn more about the general theories developed from singularly perturbed methods. Designed for PhD students and junior mathematicians intending to do their research in the area of elliptic differential equations, the text covers three main topics. The first is the compactness of the minimization sequences, or the Palais-Smale sequences, or a sequence of approximate solutions; the second is the construction of peak or bubbling solutions by using the Lyapunov-Schmidt reduction method; and the third is the local uniqueness of these solutions.

Author : Ferdinand Verhulst
Publisher : Springer Science & Business Media
ISBN 13 : 0387283137
Total Pages : 332 pages
Book Rating : 4.35/5 ( download)

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Download or read book Methods and Applications of Singular Perturbations written by Ferdinand Verhulst and published by Springer Science & Business Media. This book was released on 2006-06-04 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach

Author : Robert E. Jr. O'Malley
Publisher : Elsevier
ISBN 13 : 0323162274
Total Pages : 215 pages
Book Rating : 4.72/5 ( download)

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Download or read book Introduction to Singular Perturbations written by Robert E. Jr. O'Malley and published by Elsevier. This book was released on 2012-12-02 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : E.M. de Jager
Publisher : Elsevier
ISBN 13 : 9780080542751
Total Pages : 339 pages
Book Rating : 4.51/5 ( download)

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Download or read book The Theory of Singular Perturbations written by E.M. de Jager and published by Elsevier. This book was released on 1996-11-08 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Bernhard Kawohl
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.28/5 ( download)

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Download or read book A singular perturbation approach to nonlinear elliptic boundary value problems written by Bernhard Kawohl and published by . This book was released on 1981 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Antonio Ambrosetti
Publisher : Springer Science & Business Media
ISBN 13 : 3764373962
Total Pages : 187 pages
Book Rating : 4.62/5 ( download)

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Download or read book Perturbation Methods and Semilinear Elliptic Problems on R^n written by Antonio Ambrosetti and published by Springer Science & Business Media. This book was released on 2006-03-21 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several important problems arising in Physics, Di?erential Geometry and other n topics lead to consider semilinear variational elliptic equations on R and a great deal of work has been devoted to their study. From the mathematical point of view, the main interest relies on the fact that the tools of Nonlinear Functional Analysis, based on compactness arguments, in general cannot be used, at least in a straightforward way, and some new techniques have to be developed. n On the other hand, there are several elliptic problems on R which are p- turbative in nature. In some cases there is a natural perturbation parameter, like inthe bifurcationfromthe essentialspectrum orinsingularlyperturbed equations or in the study of semiclassical standing waves for NLS. In some other circ- stances, one studies perturbations either because this is the ?rst step to obtain global results or else because it often provides a correct perspective for further global studies. For these perturbation problems a speci?c approach,that takes advantage of such a perturbative setting, seems the most appropriate. These abstract tools are provided by perturbation methods in critical point theory. Actually, it turns out that such a framework can be used to handle a large variety of equations, usually considered di?erent in nature. Theaimofthismonographistodiscusstheseabstractmethodstogetherwith their applications to several perturbation problems, whose common feature is to n involve semilinear Elliptic Partial Di?erential Equations on R with a variational structure.

Author : Hans-Görg Roos
Publisher : Springer Science & Business Media
ISBN 13 : 3540344675
Total Pages : 599 pages
Book Rating : 4.74/5 ( download)

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Download or read book Robust Numerical Methods for Singularly Perturbed Differential Equations written by Hans-Görg Roos and published by Springer Science & Business Media. This book was released on 2008-09-17 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition incorporates new developments in numerical methods for singularly perturbed differential equations, focusing on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics.

Author : Antonio Ambrosetti
Publisher : Birkhäuser
ISBN 13 : 9783764390860
Total Pages : 184 pages
Book Rating : 4.67/5 ( download)

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Download or read book Perturbation Methods and Semilinear Elliptic Problems on R^n written by Antonio Ambrosetti and published by Birkhäuser. This book was released on 2009-09-03 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several important problems arising in Physics, Di?erential Geometry and other n topics lead to consider semilinear variational elliptic equations on R and a great deal of work has been devoted to their study. From the mathematical point of view, the main interest relies on the fact that the tools of Nonlinear Functional Analysis, based on compactness arguments, in general cannot be used, at least in a straightforward way, and some new techniques have to be developed. n On the other hand, there are several elliptic problems on R which are p- turbative in nature. In some cases there is a natural perturbation parameter, like inthe bifurcationfromthe essentialspectrum orinsingularlyperturbed equations or in the study of semiclassical standing waves for NLS. In some other circ- stances, one studies perturbations either because this is the ?rst step to obtain global results or else because it often provides a correct perspective for further global studies. For these perturbation problems a speci?c approach,that takes advantage of such a perturbative setting, seems the most appropriate. These abstract tools are provided by perturbation methods in critical point theory. Actually, it turns out that such a framework can be used to handle a large variety of equations, usually considered di?erent in nature. Theaimofthismonographistodiscusstheseabstractmethodstogetherwith their applications to several perturbation problems, whose common feature is to n involve semilinear Elliptic Partial Di?erential Equations on R with a variational structure.

Author : John J H Miller
Publisher : World Scientific
ISBN 13 : 9814452777
Total Pages : 191 pages
Book Rating : 4.79/5 ( download)

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Download or read book Fitted Numerical Methods For Singular Perturbation Problems: Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions (Revised Edition) written by John J H Miller and published by World Scientific. This book was released on 2012-02-29 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : K. W. Chang
Publisher : Springer Science & Business Media
ISBN 13 : 146121114X
Total Pages : 191 pages
Book Rating : 4.43/5 ( download)

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Download or read book Nonlinear Singular Perturbation Phenomena written by K. W. Chang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our purpose in writing this monograph is twofold. On the one hand, we want to collect in one place many of the recent results on the exist ence and asymptotic behavior of solutions of certain classes of singularly perturbed nonlinear boundary value problems. On the other, we hope to raise along the way a number of questions for further study, mostly ques tions we ourselves are unable to answer. The presentation involves a study of both scalar and vector boundary value problems for ordinary dif ferential equations, by means of the consistent use of differential in equality techniques. Our results for scalar boundary value problems obeying some type of maximum principle are fairly complete; however, we have been unable to treat, under any circumstances, problems involving "resonant" behavior. The linear theory for such problems is incredibly complicated already, and at the present time there appears to be little hope for any kind of general nonlinear theory. Our results for vector boundary value problems, even those admitting higher dimensional maximum principles in the form of invariant regions, are also far from complete. We offer them with some trepidation, in the hope that they may stimulate further work in this challenging and important area of differential equa tions. The research summarized here has been made possible by the support over the years of the National Science Foundation and the National Science and Engineering Research Council.