Constructive Methods For Linear And Nonlinear Boundary Value Problems For Analytic Functions
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Constructive Methods For Linear And Nonlinear Boundary Value Problems For Analytic Functions
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Author : v Mityushev
language : en
Publisher: CRC Press
Release Date : 1999-11-29
Constructive Methods For Linear And Nonlinear Boundary Value Problems For Analytic Functions written by v Mityushev and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-29 with Mathematics categories.
Constructive methods developed in the framework of analytic functions effectively extend the use of mathematical constructions, both within different branches of mathematics and to other disciplines. This monograph presents some constructive methods-based primarily on original techniques-for boundary value problems, both linear and nonlinear. From among the many applications to which these methods can apply, the authors focus on interesting problems associated with composite materials with a finite number of inclusions. How far can one go in the solutions of problems in nonlinear mechanics and physics using the ideas of analytic functions? What is the difference between linear and nonlinear cases from the qualitative point of view? What kinds of additional techniques should one use in investigating nonlinear problems? Constructive Methods for Linear and Nonlinear Boundary Value Problems serves to answer these questions, and presents many results to Westerners for the first time. Among the most interesting of these is the complete solution of the Riemann-Hilbert problem for multiply connected domains. The results offered in Constructive Methods for Linear and Nonlinear Boundary Value Problems are prepared for direct application. A historical survey along with background material, and an in-depth presentation of practical methods make this a self-contained volume useful to experts in analytic function theory, to non-specialists, and even to non-mathematicians who can apply the methods to their research in mechanics and physics.
Singularly Perturbed Boundary Value Problems
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Author : Matteo Dalla Riva
language : en
Publisher: Springer Nature
Release Date : 2021-10-01
Singularly Perturbed Boundary Value Problems written by Matteo Dalla Riva and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-01 with Mathematics categories.
This book is devoted to the analysis of the basic boundary value problems for the Laplace equation in singularly perturbed domains. The main purpose is to illustrate a method called Functional Analytic Approach, to describe the dependence of the solutions upon a singular perturbation parameter in terms of analytic functions. Here the focus is on domains with small holes and the perturbation parameter is the size of the holes. The book is the first introduction to the topic and covers the theoretical material and its applications to a series of problems that range from simple illustrative examples to more involved research results. The Functional Analytic Approach makes constant use of the integral representation method for the solutions of boundary value problems, of Potential Theory, of the Theory of Analytic Functions both in finite and infinite dimension, and of Nonlinear Functional Analysis. Designed to serve various purposes and readerships, the extensive introductory part spanning Chapters 1–7 can be used as a reference textbook for graduate courses on classical Potential Theory and its applications to boundary value problems. The early chapters also contain results that are rarely presented in the literature and may also, therefore, attract the interest of more expert readers. The exposition moves on to introduce the Functional Analytic Approach. A reader looking for a quick introduction to the method can find simple illustrative examples specifically designed for this purpose. More expert readers will find a comprehensive presentation of the Functional Analytic Approach, which allows a comparison between the approach of the book and the more classical expansion methods of Asymptotic Analysis and offers insights on the specific features of the approach and its applications to linear and nonlinear boundary value problems.
Nonlinear Analysis Theory And Methods
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Author : Nikolaos S. Papageorgiou
language : en
Publisher: Springer
Release Date : 2019-02-26
Nonlinear Analysis Theory And Methods written by Nikolaos S. Papageorgiou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-26 with Mathematics categories.
This book emphasizes those basic abstract methods and theories that are useful in the study of nonlinear boundary value problems. The content is developed over six chapters, providing a thorough introduction to the techniques used in the variational and topological analysis of nonlinear boundary value problems described by stationary differential operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations as well as their applications to various processes arising in the applied sciences. They show how these diverse topics are connected to other important parts of mathematics, including topology, functional analysis, mathematical physics, and potential theory. Throughout the book a nice balance is maintained between rigorous mathematics and physical applications. The primary readership includes graduate students and researchers in pure and applied nonlinear analysis.
Boundary Value Problems For Analytic Functions
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Author : Jian-ke Lu
language : en
Publisher: World Scientific
Release Date : 1994-02-04
Boundary Value Problems For Analytic Functions written by Jian-ke Lu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-02-04 with Mathematics categories.
This book deals with boundary value problems for analytic functions with applications to singular integral equations. New and simpler proofs of certain classical results such as the Plemelj formula, the Privalov theorem and the Poincaré-Bertrand formula are given. Nearly one third of this book contains the author's original works, most of which have not been published in English before and, hence, were previously unknown to most readers in the world.It consists of 7 chapters together with an appendix: Chapter I describes the basic knowledge on Cauchy-type integrals and Cauchy principal value integrals; Chapters II and III study, respectively, fundamental boundary value problems and their applications to singular integral equations for closed contours; Chapters IV and V discuss the same problems for curves with nodes (including open arcs); Chaper VI deals with similar problems for systems of functions; Chapter VII is concerned with some miscellaneous problems and the Appendix contains some basic results on Fredholm integral equations. In most sections, there are carefully selected sets of exercises, some of which supplement the text of the sections; answers/hints are also given for some of these exercises.For graduate students or seniors, all the 7 chapters can be used for a full year course, while the first 3 chapters may be used for a one-semester course.
Numerical Analytic Methods In Theory Of Boundary Value Problems
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Author : Miklos Ronto
language : en
Publisher: World Scientific
Release Date : 2000-06-30
Numerical Analytic Methods In Theory Of Boundary Value Problems written by Miklos Ronto and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-30 with Mathematics categories.
This book contains the main results of the authors' investigations on the development and application of numerical-analytic methods for ordinary nonlinear boundary value problems (BVPs). The methods under consideration provide an opportunity to solve the two important problems of the BVP theory — namely, to establish existence theorems and to build approximation solutions. They can be used to investigate a wide variety of BVPs.The Appendix, written in collaboration with S I Trofimchuk, discusses the connection of the new method with the classical Cesari, Cesari-Hale and Lyapunov-Schmidt methods.
Applied Mechanics Reviews
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Author :
language : en
Publisher:
Release Date : 1970
Applied Mechanics Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mechanics, Applied categories.
Approximate Methods And Numerical Analysis For Elliptic Complex Equation
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Author : Guo Chun Wen
language : en
Publisher: CRC Press
Release Date : 1999-06-11
Approximate Methods And Numerical Analysis For Elliptic Complex Equation written by Guo Chun Wen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-06-11 with Mathematics categories.
Numerical methods for elliptic partial differential equations have been the subject of many books in recent years, but few have treated the subject of complex equations. In this important new book, the author introduces the theory of, and approximate methods for, nonlinear elliptic complex equations in multiple connected domains. Constructive methods are systematically applied to proper boundary value problems which include very general boundary conditions. Approximate and numerical methods, such as the Newton imbedding method, the continuity method, the finite element method, the difference method and the boundary integral method, as well as their applications, are discussed in detail. The book will be of interest to all scientists studying the theory or applications of complex analysis.
An Introduction To Nonlinear Boundary Value Problems
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Author : Lakshmikantham
language : en
Publisher: Academic Press
Release Date : 1974-05-31
An Introduction To Nonlinear Boundary Value Problems written by Lakshmikantham and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-05-31 with Computers categories.
A book on an advanced level that exposes the reader to the fascinating field of differential equations and provides a ready access to an up-to-date state of this art is of immense value. This book presents a variety of techniques that are employed in the theory of nonlinear boundary value problems. For example, the following are discussed: methods that involve differential inequalities; shooting and angular function techniques; functional analytic approaches; topological methods.
Constructive Methods For Linear And Nonlinear Boundary Value Problems
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Author : Valdimir V Mityushev
language : en
Publisher:
Release Date : 1999-05-01
Constructive Methods For Linear And Nonlinear Boundary Value Problems written by Valdimir V Mityushev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-05-01 with categories.
Monogenic Functions In Spaces With Commutative Multiplication And Applications
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Author : Sergiy A. Plaksa
language : en
Publisher: Springer Nature
Release Date : 2023-07-18
Monogenic Functions In Spaces With Commutative Multiplication And Applications written by Sergiy A. Plaksa and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-18 with Mathematics categories.
This monograph develops a theory of continuous and differentiable functions, called monogenic functions, in the sense of Gateaux functions taking values in some vector spaces with commutative multiplication. The study of these monogenic functions in various commutative algebras leads to a discovery of new ways of solving boundary value problems in mathematical physics. The book consists of six parts: Part I presents some preliminary notions and introduces various concepts of differentiable mappings of vector spaces. Part II - V is devoted to the study of monogenic functions in various spaces with commutative multiplication, namely, three dimensional commutative algebras with two-dimensional radical, finite-dimensional commutative associative algebras, infinite-dimensional vector spaces associated with the three-dimensional Laplace equation and infinite-dimensional vector spaces associated with axial-symmetric potential fields. Part VI presents some boundary value problems for axial-symmetric potential fields and develops effective analytic methods of solving these boundary value problems with various applications in mathematical physics. Graduate students and researchers alike benefit from this book.