Hypersingular integral equations and their applications /
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| Author / Creator: | Lifanov, L. K. |
|---|---|
| Imprint: | London : Taylor & Francis, 2004. |
| Description: | 396 p. ; 25 cm. |
| Language: | English |
| Series: | Differential and integral equations and their applications |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/5138238 |
Table of Contents:
- Preface
- Authors
- Chapter 1.. Singular Integrals and Integral Equations
- 1.1.. Some Facts from the Theory of One-Dimensional Integrals
- 1.2.. One-Dimensional Equations
- 1.3.. Some Facts from the Theory of Multi-Dimensional Integrals
- 1.4.. Two-Dimensional Equations
- Chapter 2.. Sobolev-Slobodetskii Spaces
- 2.1.. Generalized Functions
- 2.2.. Fourier Transformation
- 2.3.. Sobolev-Slobodetskii Spaces
- 2.4.. Sobolev-Slobodetskii Spaces on Manifolds
- Chapter 3.. Hypersingular Integral Equations
- 3.1.. Pseudodifferential Operators and their Properties
- 3.2.. Changing Variables in Pseudodifferential Operators
- 3.3.. Pseudodifferential and Hypersingular Integral Equations
- Chapter 4.. Neumann Problem and Integral Equations with Double Layer Potential
- Introduction
- 4.1.. Reduction of the Neumann Problem to a Hypersingular Equation
- 4.2.. The Noetherian Property of the Prandtl Operator
- 4.3.. Index of the Prandtl Operator
- 4.4.. Equation of the Double Layer Potential in the Plane Case
- Chapter 5.. Spaces of Fractional Quotients and Their Properties
- 5.1.. Discrete Fourier Transformation and Pseudo-Difference Operators
- 5.2.. Special Trigonometric Series
- 5.3.. Spaces of Fractional Quotients M(r, h)
- 5.4.. Integral Projector
- 5.5.. Spaces M(r, h, [Omega subscript h]) and M(r, h, [Omega subscript h])
- 5.6.. Weighted Spaces
- Chapter 6.. Discrete Operators in Quotient Spaces
- 6.1.. Bounded Operator Families in Quotient Spaces M(r, h)
- 6.1.1.. One-Dimensional Discrete Singular Operators
- 6.1.2.. Multidimensional Discrete Singular Operators
- 6.1.3.. Discrete Vortex Operators
- 6.1.4.. Difference Operators
- 6.2.. Approximation of Operators
- 6.3.. Quadrature Formulas in Sobolev-Slobodetskii Spaces
- 6.3.1.. Quadrature Formulas for Integrals
- 6.3.2.. Quadrature Formulas for Singular Integrals
- 6.3.3.. Quadrature Formulas for Hypersingular Integrals
- Chapter 7.. Stability of Discrete Operators in Quotient Spaces
- 7.1.. Convergence of Approximate Solutions and the Existence of Solutions of Operator Equations
- 7.2.. Stability of Discrete Operators in Quotient Spaces
- 7.2.1.. Discrete Vortex Operators
- 7.2.2.. Iterated Difference Laplace Operator of Order m
- 7.2.3.. Hypersingular Operators
- 7.2.4.. Second Order Elliptic Difference Operator with Variable Coefficients
- 7.3.. Some Equations
- 7.3.1.. The Dirichlet Problem for the General Second Order Elliptic Equation
- 7.3.2.. Characteristic Hypersingular Equation
- 7.3.3.. Iterated Laplace Operator of Order m (the Dirichlet Problem)
- 7.3.4.. An Equation Related to Diffraction Problems
- Chapter 8.. Asymptotic Estimates of the Discrete Green Function
- 8.1.. Restriction Problems for Pseudodifference Operators
- 8.2.. Estimates of the Discrete Green Function for the Discrete Prandtl Operator in the Halfplane
- 8.3.. Estimates of the Discrete Green Function for the Prandtl Operators in Bounded Domains
- 8.4.. Asymptotic Estimates of the Discrete Green Function in Rectangular Domains
- 8.5.. Asymptotic Estimates of Special Matrices
- Chapter 9.. Quadrature Formulas for Singular and Hypersingular Integrals
- 9.1.. Integrals over a Closed Smooth Curve; Hilbert Integrals
- 9.2.. Integrals over an Open-Ended Smooth Curve
- 9.3.. Integrals Arising in Boundary Value Problems for the Laplace and the Helmholtz Equations
- 9.4.. Integrals on Smooth Surfaces with Border
- Chapter 10.. Numerical Analysis of Hypersingular Integral Equations
- 10.1.. Convergence in Quotient Spaces for Equations on a Smooth Surface with Border
- 10.2.. Neumann Problem for the Helmholtz Equation: Convergence in Quotient Spaces for the Corresponding Hypersingular Integral Equation
- 10.3.. Weak Convergence for Equations in a Plane Domain
- 10.4.. Convergence for the Multhopff Equation
- 10.5.. Convergence of the Numerical Solution in the C-Norm
- 10.6.. Convergence of Difference Ratios for the Numerical Solution
- Chapter 11.. Problems in Aerodynamics
- 11.1.. Mathematical Modelling of Flow Past an Airfoil with Suction and Pseudodifferential Operators
- 11.2.. Elements of the Potential Theory in the Plane Case
- 11.3.. Mathematical Modelling of Flow Past an Airfoil with Suction and Jet Discharge
- 11.4.. Numerical Analysis of 3D Flows Past Bodies of Arbitrary Shape
- 11.5.. Elements of the Potential Theory in the Three-Dimensional case
- 11.6.. Mathematical Modelling and Numerical Analysis of Nonstationary Flow past a Ship Deck
- Chapter 12.. Some Problems of Physics
- 12.1.. Mathematical Modelling of Wide-Band Antennas
- 12.2.. Antenna-Diffraction Problems and Current Sources on the Antenna Surface
- 12.3.. Numerical Solution of the 3D Neumann problem for the Scalar Helmholtz Equation for Bodies of Complex Shape
- 12.4.. Contact Problem: Impression of a Uniformly Moving Punch into an Elastic Halfplane with Heat Generation
- Conclusion
- References
- Index
