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Author: Elias Wegert
Publisher: Wiley-VCH
ISBN:
Category : Mathematics
Languages : en
Pages : 248
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Book Description
Covers various topics in nonlinear boundary value problems for holomorphic functions, including existence and uniqueness results, questions concerning parameter dependence, regularity theorems, several procedures for numerically solving such problems, and applications to nonlinear singular integral equations. The emphasis is mainly on geometric aspects. Numerical methods are discussed. This text requires only an elementary knowledge of function theory. Includes a 13-page bibliography. Distributed in the US by VCH. Annotation copyright by Book News, Inc., Portland, OR
Author: Elias Wegert
Publisher: Wiley-VCH
ISBN:
Category : Mathematics
Languages : en
Pages : 248
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Book Description
Covers various topics in nonlinear boundary value problems for holomorphic functions, including existence and uniqueness results, questions concerning parameter dependence, regularity theorems, several procedures for numerically solving such problems, and applications to nonlinear singular integral equations. The emphasis is mainly on geometric aspects. Numerical methods are discussed. This text requires only an elementary knowledge of function theory. Includes a 13-page bibliography. Distributed in the US by VCH. Annotation copyright by Book News, Inc., Portland, OR
Author: Jian-ke Lu
Publisher: World Scientific
ISBN: 9814518026
Category : Mathematics
Languages : en
Pages : 482
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Book Description
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.
Author: Guo Chun Wen
Publisher: World Scientific
ISBN: 981454311X
Category : Science
Languages : en
Pages : 338
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Book Description
In this proceedings volume, the following topics are discussed: (1) various boundary value problems for partial differential equations and functional equations, including free and moving boundary problems; (2) the theory and methods of integral equations and integral operators, including singular integral equations; (3) applications of boundary value problems and integral equations to mechanics and physics; (4) numerical methods of integral equations and boundary value problems; and (5) some problems related with analysis and the foregoing subjects.
Author: v Mityushev
Publisher: CRC Press
ISBN: 9781584880578
Category : Mathematics
Languages : en
Pages : 300
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Book Description
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.
Author: Guo Chun Wen
Publisher: World Scientific
ISBN: 981451831X
Category : Mathematics
Languages : en
Pages : 436
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Book Description
In this volume, we report new results about various boundary value problems for partial differential equations and functional equations, theory and methods of integral equations and integral operators including singular integral equations, applications of boundary value problems and integral equations to mechanics and physics, numerical methods of integral equations and boundary value problems, theory and methods for inverse problems of mathematical physics, Clifford analysis and related problems.Contributors include: L Baratchart, B L Chen, D C Chen, S S Ding, K Q Lan, A Farajzadeh, M G Fei, T Kosztolowicz, A Makin, T Qian, J M Rassias, J Ryan, C-Q Ru, P Schiavone, P Wang, Q S Zhang, X Y Zhang, S Y Du, H Y Gao, X Li, Y Y Qiao, G C Wen, Z T Zhang, etc.
Author: F. D. Gakhov
Publisher: Elsevier
ISBN: 1483164985
Category : Mathematics
Languages : en
Pages : 585
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Book Description
Boundary Value Problems is a translation from the Russian of lectures given at Kazan and Rostov Universities, dealing with the theory of boundary value problems for analytic functions. The emphasis of the book is on the solution of singular integral equations with Cauchy and Hilbert kernels. Although the book treats the theory of boundary value problems, emphasis is on linear problems with one unknown function. The definition of the Cauchy type integral, examples, limiting values, behavior, and its principal value are explained. The Riemann boundary value problem is emphasized in considering the theory of boundary value problems of analytic functions. The book then analyzes the application of the Riemann boundary value problem as applied to singular integral equations with Cauchy kernel. A second fundamental boundary value problem of analytic functions is the Hilbert problem with a Hilbert kernel; the application of the Hilbert problem is also evaluated. The use of Sokhotski's formulas for certain integral analysis is explained and equations with logarithmic kernels and kernels with a weak power singularity are solved. The chapters in the book all end with some historical briefs, to give a background of the problem(s) discussed. The book will be very valuable to mathematicians, students, and professors in advanced mathematics and geometrical functions.
Author: Guo Chun Wen
Publisher: World Scientific
ISBN: 9814327859
Category : Mathematics
Languages : en
Pages : 436
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Book Description
In this volume, we report new results about various boundary value problems for partial differential equations and functional equations, theory and methods of integral equations and integral operators including singular integral equations, applications of boundary value problems and integral equations to mechanics and physics, numerical methods of integral equations and boundary value problems, theory and methods for inverse problems of mathematical physics, Clifford analysis and related problems. Contributors include: L Baratchart, B L Chen, D C Chen, S S Ding, K Q Lan, A Farajzadeh, M G Fei, T Kosztolowicz, A Makin, T Qian, J M Rassias, J Ryan, C-Q Ru, P Schiavone, P Wang, Q S Zhang, X Y Zhang, S Y Du, H Y Gao, X Li, Y Y Qiao, G C Wen, Z T Zhang, etc.
Author: Heinrich Begehr
Publisher: Springer Science & Business Media
ISBN: 1461332761
Category : Mathematics
Languages : en
Pages : 367
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Book Description
This volume of the Proceedings of the congress ISAAC '97 collects the con tributions of the four sections 1. Function theoretic and functional analytic methods for pde, 2. Applications of function theory of several complex variables to pde, 3. Integral equations and boundary value problems, 4. Partial differential equations. Most but not all of the authors have participated in the congress. Unfortunately some from Eastern Europe and Asia have not managed to come because of lack of financial support. Nevertheless their manuscripts of the proposed talks are included in this volume. The majority of the papers deal with complex methods. Among them boundary value problems in particular the Riemann-Hilbert, the Riemann (Hilbert) and related problems are treated. Boundary behaviour of vector-valued functions are studied too. The Riemann-Hilbert problem is solved for elliptic complex equations, for mixed complex equations, and for several complex variables. It is considered in a general topological setting for mappings into q;n and related to Toeplitz operators. Convolution operators are investigated for nilpotent Lie groups leading to some consequences for the null space of the tangential Cauchy Riemann operator. Some boundary value problems for overdetermined systems in balls of q;n are solved explicitly. A survey is given for the Gauss-Manin connection associated with deformations of curve singularities. Several papers deal with generalizations of analytic functions with various applications to mathematical physics. Singular integrals in quaternionic anal ysis are studied which are applied to the time-harmonic Maxwell equations.
Author: Georgii S Litvinchuk
Publisher:
ISBN: 9789401143646
Category :
Languages : en
Pages : 402
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Book Description
Author: D. B. Ingham
Publisher: Springer Science & Business Media
ISBN: 3642823300
Category : Technology & Engineering
Languages : en
Pages : 165
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Book Description
Harmonic and biharmonic boundary value problems (BVP) arising in physical situations in fluid mechanics are, in general, intractable by analytic techniques. In the last decade there has been a rapid increase in the application of integral equation techniques for the numerical solution of such problems [1,2,3]. One such method is the boundary integral equation method (BIE) which is based on Green's Formula [4] and enables one to reformulate certain BVP as integral equations. The reformulation has the effect of reducing the dimension of the problem by one. Because discretisation occurs only on the boundary in the BIE the system of equations generated by a BIE is considerably smaller than that generated by an equivalent finite difference (FD) or finite element (FE) approximation [5]. Application of the BIE in the field of fluid mechanics has in the past been limited almost entirely to the solution of harmonic problems concerning potential flows around selected geometries [3,6,7]. Little work seems to have been done on direct integral equation solution of viscous flow problems. Coleman [8] solves the biharmonic equation describing slow flow between two semi infinite parallel plates using a complex variable approach but does not consider the effects of singularities arising in the solution domain. Since the vorticity at any singularity becomes unbounded then the methods presented in [8] cannot achieve accurate results throughout the entire flow field.
