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Complex Analytic Methods For Partial Differential Equations

Complex Analytic Methods For Partial Differential Equations
Author: Heinrich G W Begehr
Publisher: World Scientific Publishing Company
ISBN: 9813104686
Size: 77.31 MB
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This is an introductory text for beginners who have a basic knowledge of complex analysis, functional analysis and partial differential equations. Riemann and Riemann-Hilbert boundary value problems are discussed for analytic functions, for inhomogeneous Cauchy-Riemann systems as well as for generalized Beltrami systems. Related problems such as the Poincaré problem, pseudoparabolic systems and complex elliptic second order equations are also considered. Estimates for solutions to linear equations existence and uniqueness results are thus available for related nonlinear problems; the method is explained by constructing entire solutions to nonlinear Beltrami equations. Often problems are discussed just for the unit disc but more general domains, even of multiply connectivity, are involved.
Complex Analytic Methods for Partial Differential Equations
Language: en
Pages: 284
Authors: Heinrich G W Begehr
Categories: Mathematics
Type: BOOK - Published: 1994-11-15 - Publisher: World Scientific Publishing Company
This is an introductory text for beginners who have a basic knowledge of complex analysis, functional analysis and partial differential equations. Riemann and Riemann-Hilbert boundary value problems are discussed for analytic functions, for inhomogeneous Cauchy-Riemann systems as well as for generalized Beltrami systems. Related problems such as the Poincaré problem, pseudoparabolic systems and complex elliptic second order equations are also considered. Estimates for solutions to linear equations existence and uniqueness results are thus available for related nonlinear problems; the method is explained by constructing entire solutions to nonlinear Beltrami equations. Often problems are discussed just for the unit disc but more general domains, even of multiply connectivity, are involved.
Analytic Methods for Partial Differential Equations
Language: en
Pages: 316
Authors: G. Evans, J. Blackledge, P. Yardley
Categories: Mathematics
Type: BOOK - Published: 1999-11-01 - Publisher: Springer Science & Business Media
This is the practical introduction to the analytical approach taken in Volume 2. Based upon courses in partial differential equations over the last two decades, the text covers the classic canonical equations, with the method of separation of variables introduced at an early stage. The characteristic method for first order equations acts as an introduction to the classification of second order quasi-linear problems by characteristics. Attention then moves to different co-ordinate systems, primarily those with cylindrical or spherical symmetry. Hence a discussion of special functions arises quite naturally, and in each case the major properties are derived. The next section deals with the use of integral transforms and extensive methods for inverting them, and concludes with links to the use of Fourier series.
Complex Methods for Partial Differential Equations
Language: en
Pages: 334
Authors: Heinrich Begehr, A. Okay Celebi, W. Tutschke
Categories: Mathematics
Type: BOOK - Published: 2013-12-01 - Publisher: Springer Science & Business Media
This volume is a collection of manscripts mainly originating from talks and lectures given at the Workshop on Recent Trends in Complex Methods for Par tial Differential Equations held from July 6 to 10, 1998 at the Middle East Technical University in Ankara, Turkey, sponsored by The Scientific and Tech nical Research Council of Turkey and the Middle East Technical University. This workshop is a continuation oftwo workshops from 1988 and 1993 at the In ternational Centre for Theoretical Physics in Trieste, Italy entitled Functional analytic Methods in Complex Analysis and Applications to Partial Differential Equations. Since classical complex analysis of one and several variables has a long tra dition it is of high level. But most of its basic problems are solved nowadays so that within the last few decades it has lost more and more attention. The area of complex and functional analytic methods in partial differential equations, however, is still a growing and flourishing field, in particular as these methods are not only applied. Whithin the framework of holomorphic functions but are also combined with properties of generalized analytic functions. This can be seen by the many books which recently were published in this field and also
Complex Analytic Methods for Partial Differential Equations
Language: en
Pages: 273
Authors: Heinrich G. W. Begehr
Categories: Mathematics
Type: BOOK - Published: 1994 - Publisher: World Scientific
This is an introductory text for beginners who have a basic knowledge of complex analysis, functional analysis and partial differential equations. Riemann and Riemann-Hilbert boundary value problems are discussed for analytic functions, for inhomogeneous Cauchy-Riemann systems as well as for generalized Beltrami systems. Related problems such as the Poincar‚ problem, pseudoparabolic systems and complex elliptic second order equations are also considered. Estimates for solutions to linear equations existence and uniqueness results are thus available for related nonlinear problems; the method is explained by constructing entire solutions to nonlinear Beltrami equations. Often problems are discussed just for the unit disc but more general domains, even of multiply connectivity, are involved.
Partial Differential and Integral Equations
Language: en
Pages: 384
Authors: Heinrich Begehr, R.P. Gilbert, Wen-Chung Guo
Categories: Mathematics
Type: BOOK - Published: 2013-12-01 - Publisher: Springer Science & Business Media
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
Functional Analytic Methods In Complex Analysis And Applications To Partial Differential Equations
Language: en
Pages: 440
Authors: Mshimba A S A, Tutschke Wolfgang
Categories: Mathematics
Type: BOOK - Published: 1995-10-17 - Publisher: World Scientific
Books about Functional Analytic Methods In Complex Analysis And Applications To Partial Differential Equations
Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations
Language: en
Pages: 300
Authors: Bert-Wolfgang Schulze, M. W. Wong
Categories: Mathematics
Type: BOOK - Published: 2010-03-01 - Publisher: Springer Science & Business Media
Consists of the expository paper based on the 6-hour minicourse given by Professor Bert-Wolfgang Schulze, and sixteen papers based on lectures given at the workshop and on invitations.
Approximate Methods and Numerical Analysis for Elliptic Complex Equation
Language: en
Pages: 248
Authors: Guo Chun Wen
Categories: Mathematics
Type: BOOK - Published: 1999-06-11 - Publisher: CRC Press
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.
Methods for Constructing Exact Solutions of Partial Differential Equations
Language: en
Pages: 352
Authors: Sergey V. Meleshko
Categories: Technology & Engineering
Type: BOOK - Published: 2006-06-18 - Publisher: Springer Science & Business Media
Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.
Proceedings of the functional analytic methods in complex analysis and applications to partial differential equations
Language: en
Pages: 428
Authors: Ali Seif Mshimba
Categories: Technology & Engineering
Type: BOOK - Published: 1995 - Publisher:
Books about Proceedings of the functional analytic methods in complex analysis and applications to partial differential equations