Singularly Perturbed Methods For Nonlinear Elliptic Problems PDF Download
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Author | : Daomin Cao |
Publisher | : Cambridge University Press |
Total Pages | : 263 |
Release | : 2021-02-18 |
Genre | : Mathematics |
ISBN | : 1108858473 |
Download Singularly Perturbed Methods for Nonlinear Elliptic Problems Book in PDF, ePub and Kindle
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 | : Daomin Cao |
Publisher | : Cambridge University Press |
Total Pages | : 263 |
Release | : 2021-02-18 |
Genre | : Mathematics |
ISBN | : 1108836836 |
Download Singularly Perturbed Methods for Nonlinear Elliptic Problems Book in PDF, ePub and Kindle
A systematic introduction to the singularly perturbed methods in the study of concentration solutions for nonlinear elliptic problems.
Author | : Ferdinand Verhulst |
Publisher | : Springer Science & Business Media |
Total Pages | : 332 |
Release | : 2006-06-04 |
Genre | : Mathematics |
ISBN | : 0387283137 |
Download Methods and Applications of Singular Perturbations Book in PDF, ePub and Kindle
Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach
Author | : E.M. de Jager |
Publisher | : Elsevier |
Total Pages | : 353 |
Release | : 1996-11-08 |
Genre | : Mathematics |
ISBN | : 0080542751 |
Download The Theory of Singular Perturbations Book in PDF, ePub and Kindle
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 | : Lutz Tobiska |
Publisher | : |
Total Pages | : 22 |
Release | : 1982 |
Genre | : |
ISBN | : |
Download Singularly Perturbed Nonlinear Elliptic Problems of Second Order Book in PDF, ePub and Kindle
Author | : Antonio Ambrosetti |
Publisher | : Springer Science & Business Media |
Total Pages | : 187 |
Release | : 2006-03-21 |
Genre | : Mathematics |
ISBN | : 3764373962 |
Download Perturbation Methods and Semilinear Elliptic Problems on R^n Book in PDF, ePub and Kindle
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 |
Total Pages | : 191 |
Release | : 2012-02-29 |
Genre | : Mathematics |
ISBN | : 9814452777 |
Download Fitted Numerical Methods For Singular Perturbation Problems: Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions (Revised Edition) Book in PDF, ePub and Kindle
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 | : Antonio Ambrosetti |
Publisher | : Birkhäuser |
Total Pages | : 184 |
Release | : 2009-09-03 |
Genre | : Mathematics |
ISBN | : 9783764390860 |
Download Perturbation Methods and Semilinear Elliptic Problems on R^n Book in PDF, ePub and Kindle
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 |
Total Pages | : 599 |
Release | : 2008-09-17 |
Genre | : Mathematics |
ISBN | : 3540344675 |
Download Robust Numerical Methods for Singularly Perturbed Differential Equations Book in PDF, ePub and Kindle
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 | : R.S. Johnson |
Publisher | : Springer Science & Business Media |
Total Pages | : 305 |
Release | : 2005-12-28 |
Genre | : Technology & Engineering |
ISBN | : 0387232176 |
Download Singular Perturbation Theory Book in PDF, ePub and Kindle
The importance of mathematics in the study of problems arising from the real world, and the increasing success with which it has been used to model situations ranging from the purely deterministic to the stochastic, is well established. The purpose of the set of volumes to which the present one belongs is to make available authoritative, up to date, and self-contained accounts of some of the most important and useful of these analytical approaches and techniques. Each volume provides a detailed introduction to a specific subject area of current importance that is summarized below, and then goes beyond this by reviewing recent contributions, and so serving as a valuable reference source. The progress in applicable mathematics has been brought about by the extension and development of many important analytical approaches and techniques, in areas both old and new, frequently aided by the use of computers without which the solution of realistic problems would otherwise have been impossible.