Constructive Methods for Linear and Nonlinear Boundary Value Problems for Analytic Functions

Constructive Methods for Linear and Nonlinear Boundary Value Problems for Analytic Functions : Theory and Applications

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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.show more

Product details

  • Hardback | 296 pages
  • 154.4 x 244.9 x 22.4mm | 594.22g
  • Taylor & Francis Inc
  • CRC Press Inc
  • Bosa Roca, United States
  • English
  • 1584880570
  • 9781584880578

Review quote

"The book contains several fresh results and collects material which has been spread in the literature (frequently in Russian, but also from the western schools). With an extensive bibliography of about 300 items, it can serve as a reference text. The presentation is addressed to beginners and experts as well. Since the essential prerequisites are included it should be convenient to use for interested applied scientists with some mathematical background." -Elias Wegert, in Mathematical Reviews, Issue 2001d Promo Copyshow more

Table of contents

A HISTORICAL SURVEY NOTATIONS AND AUXILIARY RESULTS Geometry of Complex Plane Functional Spaces Operator Equations in Functional Spaces Properties of Analytic and Harmonic Functions Cauchy-Type Integral and Singular Integrals Schwarz Operator C-Linear Conjugation Problem Riemann-Hilbert Boundary Value Problem Entire Function Conformal Mappings R-Linear Problem and its Applications Notes and Comments NONLINEAR BOUNDARY VALUE PROBLEMS Conjugation Problem of Power Type Problem of Multiplication Type Entire Functions Methods General Riemann-Hilbert Problem of Power Type The Modulus Problem and its Generalization Linear Fractional Problem Cherepanov's Mixed Problem Notes and Comments METHOD OF FUNCTIONAL EQUATIONS Dirichlet Problem for a Doubly Connected Domain A Nonlinear Boundary Value Problem Linear Functional Equations Harmonic Measures and Schwarz Operator Linear Riemann-Hilbert Porblem Poincare Series Mixed Problem for Multiply Connected Domains Circular Polygons with Zero Angles Generalized Method of Schwarz and other Methods Notes and Comments NONLINEAR PROBLEMS OF MECHANICS Steady Heat Conduction: Nonlinear Composites Linearized Problem Constructive Solution to Integral Equations Composite Materials with Reactive Inclusions Steady Heat Conduction on Configurations An Elastic Problem for Composite Materials Plane Stokes Flow Notes and Comments BIBLIOGRAPHY INDEXshow more