邊界積分-微分方程方法的數學基礎-英文版韓厚德殷東生 9787302664734 【台灣高等教育出版社】

Name: 邊界積分-微分方程方法的數學基礎-英文版 韓厚德 殷東生 9787302664734 【台灣高等教育出版社】
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原出版社：清華大學

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書名：邊界積分-微分方程方法的數學基礎-英文版
ISBN：9787302664734
出版社：清華大學
著編譯者：韓厚德殷東生
頁數：306
所在地：中國大陸 *此為代購商品
書號：1653476
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內容簡介

本書主要討論邊界積分-微分方程的數學基礎理論，主要集中於把傳統的邊界積分方程中的超奇異積分轉化為帶弱奇性的邊界積分-微分方程。本書簡要地介紹了分佈理論，而邊界積分方程方法是基於線性偏微分方程基本解的，所以對微分方程的基本解也做了較為詳細的介紹。在餘下的章節里，本書依次討論了Laplace方程、Helmholtz方程、Navier方程組、Stokes方程等邊界積分-微分方程方法和理論。還討論了某系非線性方程如：如熱輻射、變分不等式和Steklov特徵值問題的邊界積分-微分方程理論。最後討論了有限元和邊界元的對稱耦合問題。本書可供計算數學與機械工程相關領域的研究人員和研究生參考使用。

Chapter 1 Distributions
1 1 Space of Test Functions
1 2 Definition of Distributions and Their Operations
1 3 Direct Products and Convolution of Distributions
1 4 Tempered Distributions and Fourier Transform
References
Chapter 2 Fundamental Solutions of Linear Differential Operators
2 1 Definition of Fundamental Solution
2 2 Elliptic Operators
2 2 1 Laplace Operator
2 2 2 Helmholtz Operator
2 2 3 Biharmonic Operator
2 3 Transient Operator
2 3 1 Heat Conduction Operator
2 3 2 Schr?dinger Operator
2 3 3 Wave Operator
2 4 Matrix Operator
2 4 1 Steady-State Navier Operator
2 4 2 Harmonic Navier Operator
2 4 3 Steady-State Stokes Operator
2 4 4 Steady-State Oseen Operator
References
Chapter 3 Boundary Value Problems of the Laplace Equation
3 1 Function Spaces
3 1 1 Continuous and Continuously Differential Function Spaces
3 1 2 H?lder Spaces
3 1 3 The Spaces
3 1 4 Sobolev Spaces
3 2 The Dirichlet and Neumann Problems of the Laplace Equation
3 2 1 Classical Solutions
3 2 2 Generalized Solutions and Variational Problems
3 3 Single Layer and Double Layer Potentials
3 3 1 Weakly Singular Integral Operators on
3 3 2 Double Layer Potentials
3 3 3 Single Layer Potentials
3 3 4 The Derivatives of Single Layer Potentials
3 3 5 The Derivatives of Double Layer Potentials
3 3 6 The Single and Double Layer Potentials in Sobolev Spaces
3 4 Boundary Reduction
3 4 1 Boundary Integral (Integro-Differential) Equations of the First Kind
3 4 2 Solvability of First Kind Integral Equation with n=2 and the Degenerate Scale
3 4 3 Boundary Integral Equations of the Second Kind
References
Chapter 4 Boundary Value Problems of Modified Helmholtz Equation
4 1 The Dirichlet and Neumann Boundary Problems of Modified Helmholtz Equation
4 2 Single and Double Layer Potentials of Modified Helmholtz Operator for the Continuous Densities
4 3 Single Layer Potential and Double Layer Potential in Soblov Spaces
4 4 Boundary Reduction for the Boundary Value Problems of Modified Helmholtz Equation
4 4 1 Boundary Integral Equation and Integro-Differential Equation of the First Kind
4 4 2 Boundary Integral Equations of the Second Kind
References
Chapter 5 Boundary Value Problems of Helmholtz Equation
5 1 Interior and Exterior Boundary Value Problems of Helmholtz Equation
5 2 Single and Double Layers Potentials of Helmholtz Equation
5 2 1 Single Layer Potential
5 2 2 The Double Layer Potential
5 3 Boundary Reduction for the Principal Boundary Value Problems of Helmholtz Equation
5 3 1 Boundary Integral Equation of the First Kind
5 3 2 Boundary Integro-Differential Equations of the First Kind
5 3 3 Boundary Integral Equations of the Second Kind
5 3 4 Modified Integral and Integro-Differential Equations
5 4 The Boundary Integro-Differential Equation Method for Interior Dirichlet and Neumann Eigenvalue Problems of Laplace Operator
5 4 1 Interior Dirichlet Eigenvalue Problems of Laplace Operator
5 4 2 Interior Neuamann Eigenvalue Problem of Laplace Operator
References
Chapter 6 Boundary Value Problems of the Navier Equations
6 1 Some Basic Boundary Value Problems
6 2 Single and Double Layer Potentials of the Navier System
6 2 1 Single Layer Potential
6 2 2 Double Layer Potential
6 2 3 The Derivatives of the Single Layer Potential
6 2 4 The Derivatives of the Double Layer Potential
6 2 5 The Layer Potentials and in Sobolev Spaces
6 3 Boundary Reduction for the Boundary Value Problems of the Navier System
6 3 1 First Kind Integral (Differential-integro-differential) Equations of the Boundary Value Problems of the Navier System
6 3 2 Solvability of the First Kind Integral Equations with n = 2 and the Degenerate Scales
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