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

Author: v Mityushev
Publisher: CRC Press
ISBN: 9781584880578
Format: PDF, Mobi
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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.

Progress in Analysis

Author: Heinrich G W Begehr
Publisher: World Scientific
ISBN: 9814485233
Format: PDF
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The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting. Contents: Volume 1: Function Spaces and Fractional Calculus (V I Burenkov & S Samko)Asymptotic Decomposition (Methods of Small Parameters, Averaging Theory) (J A Dubinski)Integral Transforms and Applications (S Saitoh et al.)Analytic Functionals, Hyperfunctions and Generalized Functions (M Morimoto & H Komatsu)Geometric Function Theory (G Kohr & M Kohr)omplex Function Spaces (R Aulaskari & I Laine)Value Distribution Theory and Complex Dynamics (C C Yang)Clifford Analysis (K Gürlebeck et al.)Octonions (T Dray & C Monogue)Nonlinear Potential Theory (O Martio)Classical and Fine Potential Theory, Holomorphic and Finely Holomorphic Functions (P Tamrazov)Differential Geometry and Control Theory for PDEs (B Gulliver et al.)Differential Geometry and Quantum Physics (-)Dynamical Systems (B Fiedler)Attractors for Partial Differential Equations (G Raugel)Spectral Theory of Differential Operators (B Vainberg)Pseudodifferential Operators, Quantization and Signal Analysis (M W Wong)Microlocal Analysis (B-W Schulze & M Korey) Volume 2: Complex and Functional Analytic Methods in PDEs (A Cialdea et al.)Geometric Properties of Solutions of PDEs (R Magnanini)Qualitative Properties of Solutions of Hyperbolic and Schrödinger Equations (M Reissig & K Yagdjian)Homogenization Moving Boundaries and Porous Media (A Bourgeat & R P Gilbert)Constructive Methods in Applied Problems (P Krutitskii)Waves in Complex Media (R P Gilbert & A Wirgin)Nonlinear Waves (I Lasiecka & H Koch)Mathematical Analysis of Problems in Solid Mechanics (K Hackl & X Li)Direct and Inverse Scattering (L Fishman)Inverse Problems (G N Makrakis et al.)Mathematical Methods in Non-Destructive Evaluation and Non-Destructive Testing (A Wirgin)Numerical Methods for PDEs, Systems and Optimization (A Ben-Israel & I Herrera) Readership: Graduate students and researchers in real, complex, numerical analysis, as well as mathematical physics.Keywords:Fractional Calculus;Function Theory;Potential Theory;Dynamical Systems;Differential Operators;Pseudodifferntial Operators;Partial Differential Equations;Inverse Problems

Progress in Analysis

Author: Heinrich G. W. Begehr
Publisher: World Scientific
ISBN: 981238572X
Format: PDF, ePub, Mobi
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The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting.

Nonlinear Solid Mechanics

Author: Adnan Ibrahimbegovic
Publisher: Springer Science & Business Media
ISBN: 9048123305
Format: PDF
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This book offers a recipe for constructing the numerical models for representing the complex nonlinear behavior of structures and their components, represented as deformable solid bodies. Its appeal extends to those interested in linear problems of mechanics.

Complex Analytic Methods for Partial Differential Equations

Author: Heinrich G. W. Begehr
Publisher: World Scientific
ISBN: 9789810215507
Format: PDF, ePub
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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 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.