Description
Book SynopsisConstructive 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.
Trade Review"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
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Table of ContentsA HISTORICAL SURVEYNOTATIONS AND AUXILIARY RESULTSGeometry of Complex PlaneFunctional SpacesOperator Equations in Functional SpacesProperties of Analytic and Harmonic FunctionsCauchy-Type Integral and Singular IntegralsSchwarz OperatorC-Linear Conjugation ProblemRiemann-Hilbert Boundary Value ProblemEntire FunctionConformal MappingsR-Linear Problem and its ApplicationsNotes and CommentsNONLINEAR BOUNDARY VALUE PROBLEMSConjugation Problem of Power TypeProblem of Multiplication TypeEntire Functions MethodsGeneral Riemann-Hilbert Problem of Power TypeThe Modulus Problem and its GeneralizationLinear Fractional ProblemCherepanov's Mixed ProblemNotes and CommentsMETHOD OF FUNCTIONAL EQUATIONSDirichlet Problem for a Doubly Connected DomainA Nonlinear Boundary Value ProblemLinear Functional EquationsHarmonic Measures and Schwarz OperatorLinear Riemann-Hilbert PorblemPoincaré SeriesMixed Problem for Multiply Connected DomainsCircular Polygons with Zero AnglesGeneralized Method of Schwarz and other MethodsNotes and CommentsNONLINEAR PROBLEMS OF MECHANICSSteady Heat Conduction: Nonlinear CompositesLinearized ProblemConstructive Solution to Integral EquationsComposite Materials with Reactive InclusionsSteady Heat Conduction on ConfigurationsAn Elastic Problem for Composite MaterialsPlane Stokes FlowNotes and CommentsBIBLIOGRAPHYINDEX
