Complex Methods For Partial Differential Equations

Author : Heinrich Begehr,A. Okay Celebi,W. Tutschke
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 52,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461332916

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Complex Methods for Partial Differential Equations by Heinrich Begehr,A. Okay Celebi,W. Tutschke Pdf

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 by the proceedings in this ISAAC series and the ISAAC congresses and workshops.

Author : Heinrich G. W. Begehr
Publisher : World Scientific
Page : 288 pages
File Size : 45,5 Mb
Release : 1994
Category : Mathematics
ISBN : 9810215509

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Complex Analytic Methods for Partial Differential Equations by Heinrich G. W. Begehr Pdf

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.

Author : So-chin Chen,Mei-Chi Shaw
Publisher : American Mathematical Soc.
Page : 396 pages
File Size : 44,7 Mb
Release : 2001
Category : Mathematics
ISBN : 0821829610

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Partial Differential Equations in Several Complex Variables by So-chin Chen,Mei-Chi Shaw Pdf

This book is intended as both an introductory text and a reference book for those interested in studying several complex variables in the context of partial differential equations. In the last few decades, significant progress has been made in the study of Cauchy-Riemann and tangential Cauchy-Riemann operators; this progress greatly influenced the development of PDEs and several complex variables. After the background material in complex analysis is developed in Chapters 1 to 3, thenext three chapters are devoted to the solvability and regularity of the Cauchy-Riemann equations using Hilbert space techniques. The authors provide a systematic study of the Cauchy-Riemann equations and the \bar\partial-Neumann problem, including Hórmander's L2 existence progress on the globalregularity and irregularity of the \bar\partial-Neumann operators. The second part of the book gives a comprehensive study of the tangential Cauchy-Riemann equations, another important class of equations in several complex variables first studied by Lewy. An up-to-date account of the L2 theory for \bar\partial b operator is given. Explicit integral solution representations are constructed both on the Heisenberg groups and on strictly convex boundaries with estimates in Hölder and L2spaces. Embeddability of abstract CR structures is discussed in detail here for the first time.Titles in this series are co-published with International Press, Cambridge, MA.

Author : Manfred Kracht,Erwin Kreyszig
Publisher : New York ; Toronto : Wiley
Page : 424 pages
File Size : 40,6 Mb
Release : 1988
Category : Mathematics
ISBN : UCAL:B4406640

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Methods of Complex Analysis in Partial Differential Equations with Applications by Manfred Kracht,Erwin Kreyszig Pdf

This book is devoted to the development of complex function theoretic methods in partial differential equations and to the study of analytic behaviour of solutions. It presents basic facts of the subject and includes recent results, emphasizing the method of integral operators and the method of differential operators. The first chapter gives a motivation for and the underlying ideas of, the later chapters. Chapters 2 to 7 give a detailed exposition of the basic concepts and fundamental theorems, as well as their most recent development. Chapters 8 to 13 are concerned with the application of the theory to three important classes of differential equations of mathematical physics.

Author : H. F. Weinberger
Publisher : Courier Corporation
Page : 482 pages
File Size : 55,7 Mb
Release : 2012-04-20
Category : Mathematics
ISBN : 9780486132044

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A First Course in Partial Differential Equations by H. F. Weinberger Pdf

Suitable for advanced undergraduate and graduate students, this text presents the general properties of partial differential equations, including the elementary theory of complex variables. Solutions. 1965 edition.

Author : Nakhlé H. Asmar,Gregory C. Jones
Publisher : Unknown
Page : 904 pages
File Size : 45,9 Mb
Release : 2002
Category : Mathematics
ISBN : UVA:X004635768

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Applied Complex Analysis with Partial Differential Equations by Nakhlé H. Asmar,Gregory C. Jones Pdf

This reader-friendly book presents traditional material using a modern approach that invites the use of technology. Abundant exercises, examples, and graphics make it a comprehensive and visually appealing resource. Chapter topics include complex numbers and functions, analytic functions, complex integration, complex series, residues: applications and theory, conformal mapping, partial differential equations: methods and applications, transform methods, and partial differential equations in polar and spherical coordinates. For engineers and physicists in need of a quick reference tool.

Author : Steven G. Krantz
Publisher : CRC Press
Page : 322 pages
File Size : 45,9 Mb
Release : 1992-07-02
Category : Mathematics
ISBN : 0849371554

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Partial Differential Equations and Complex Analysis by Steven G. Krantz Pdf

Ever since the groundbreaking work of J.J. Kohn in the early 1960s, there has been a significant interaction between the theory of partial differential equations and the function theory of several complex variables. Partial Differential Equations and Complex Analysis explores the background and plumbs the depths of this symbiosis. The book is an excellent introduction to a variety of topics and presents many of the basic elements of linear partial differential equations in the context of how they are applied to the study of complex analysis. The author treats the Dirichlet and Neumann problems for elliptic equations and the related Schauder regularity theory, and examines how those results apply to the boundary regularity of biholomorphic mappings. He studies the ?-Neumann problem, then considers applications to the complex function theory of several variables and to the Bergman projection.

Author : A S A Mshimba,Wolfgang Tutschke
Publisher : World Scientific
Page : 442 pages
File Size : 46,5 Mb
Release : 1995-10-17
Category : Electronic
ISBN : 9789814548533

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Functional Analytic Methods In Complex Analysis And Applications To Partial Differential Equations by A S A Mshimba,Wolfgang Tutschke Pdf

These proceedings concentrate on recent results in the following fields of complex analysis: complex methods for solving boundary value problems with piecewise smooth boundary data, complex methods for linear and nonlinear differential equations and systems of second order, and applications of scales of Banach spaces to initial value problems.Some problems in higher dimensions (such as the unification of global and local existence theorems for holomorphic functions and an elementary approach to Clifford analysis) are also discussed.Particular emphasis is placed on Symbolic Computation in Complex Analysis and on the new approaches to teach mathematical analysis based on interactions between complex analysis and partial differential equations.

Author : David A. Kopriva
Publisher : Springer Science & Business Media
Page : 397 pages
File Size : 46,7 Mb
Release : 2009-05-27
Category : Mathematics
ISBN : 9789048122615

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Implementing Spectral Methods for Partial Differential Equations by David A. Kopriva Pdf

This book explains how to solve partial differential equations numerically using single and multidomain spectral methods. It shows how only a few fundamental algorithms form the building blocks of any spectral code, even for problems with complex geometries.

Author : Heinrich Begehr,R.P. Gilbert,Wen-Chung Guo
Publisher : Springer Science & Business Media
Page : 367 pages
File Size : 55,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461332763

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Partial Differential and Integral Equations by Heinrich Begehr,R.P. Gilbert,Wen-Chung Guo Pdf

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 : H Begehr,Alan Jeffrey
Publisher : Chapman and Hall/CRC
Page : 232 pages
File Size : 42,5 Mb
Release : 1992-11-02
Category : Mathematics
ISBN : 0582096405

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Partial Differential Equations With Complex Analysis by H Begehr,Alan Jeffrey Pdf

A collection of papers on function theory and function-theoretic methods in PDEs. Results are obtained using a variety of complex analytic methods e.g. Bergman and Vekua, geometric function theory and the Riemann-Hilbert boundary value problem.

Author : Claudio I. Withalm
Publisher : De Gruyter Akademie Forschung
Page : 264 pages
File Size : 54,5 Mb
Release : 1989
Category : Differential equations, Partial
ISBN : UCAL:B2507983

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Complex Methods on Partial Differential Equations by Claudio I. Withalm Pdf

Author : Claudio I. Withalm
Publisher : Mathematical Research
Page : 0 pages
File Size : 46,8 Mb
Release : 1990-01-14
Category : Electronic
ISBN : 3112530454

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Complex Methods on Partial Differential Equations by Claudio I. Withalm Pdf

Author : Sergey V. Meleshko
Publisher : Springer Science & Business Media
Page : 367 pages
File Size : 50,6 Mb
Release : 2006-06-18
Category : Technology & Engineering
ISBN : 9780387252650

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Methods for Constructing Exact Solutions of Partial Differential Equations by Sergey V. Meleshko Pdf

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.

Author : Helmut Florian
Publisher : World Scientific
Page : 473 pages
File Size : 55,9 Mb
Release : 2001
Category : Mathematics
ISBN : 9789812794550

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Functional-analytic and Complex Methods, Their Interactions, and Applications to Partial Differential Equations by Helmut Florian Pdf

Functional analysis is not only a tool for unifying mathematical analysis, but it also provides the background for today''s rapid development of the theory of partial differential equations. Using concepts of functional analysis, the field of complex analysis has developed methods (such as the theory of generalized analytic functions) for solving very general classes of partial differential equations. This book is aimed at promoting further interactions of functional analysis, partial differential equations, and complex analysis including its generalizations such as Clifford analysis. New interesting problems in the field of partial differential equations concern, for instance, the Dirichlet problem for hyperbolic equations. Applications to mathematical physics address mainly Maxwell''s equations, crystal optics, dynamical problems for cusped bars, and conservation laws. Sample Chapter(s). Hyperbolic Equations, Waves and the Singularity Theory (858 KB). Contents: Boundary Value Problems and Initial Value Problems for Partial Differential Equations; Applications of Functional-Analytic and Complex Methods to Mathematical Physics; Partial Complex Differential Equations in the Plane; Complex Methods in Higher Dimensions. Readership: Researchers, lecturers and graduate students in the fields of analysis & differential equations, applied mathematics and mathematical physics.