《非線性複分析及其套用(英文版)》是一本數學專著，主要介紹作者們用複分析方法處理非線性一致橢圓型、拋物型、雙曲型和混合（橢圓-雙曲）型複方程及帶拋物退化線的非線性橢圓型、雙曲型和混合型複方程系統的研究成果。全書共分七章。第一至三章主要介紹一階、二階和四階非線性橢圓型複方程與方程組解的性質和各種邊值問題，其中也包含帶拋物退化線的一階和二階非線性橢圓型複方程及間斷Riemann-Hilbert邊值問題與間斷斜微商邊值問題。第四章主要介紹二階非線性(非散度型)拋物型複方程與方程組的一些邊值問題，其中包括一種非正則初-斜微商邊值問題。第五章主要介紹一階和二階非線性雙曲型複方程的一些邊值問題，而第六章主要介紹一階和二階帶拋物退化線的非線性混合型複方程的一些邊值問題，這種二階混合型方程包含空氣動力學中著名的Chaplygin 方程作為特殊情況，而邊值問題包括Tricomi 問題，Frankl問題和斜微商問題等. 第七章主要介紹上述理論和方法在非線性力學邊值問題中的套用。
基本介紹
- 書名：非線性複分析及其套用
- 出版社：科學出版社
- 頁數：447頁
- 開本：16
- 定價：86.00
- 作者：聞國椿
- 出版日期：2008年5月19日
- 語種：簡體中文
- ISBN：9787030212962
- 品牌：科學出版社
內容簡介,圖書目錄,
內容簡介
《非線性複分析及其套用(英文版)》是由科學出版社出版的。
圖書目錄
Preface
Chapter 1 Nonlinear Elliptic Complex Equations of First Order
1.1 Discontinuous Riemann-Hilbert Problem for Nonlinear Uniformly
Elliptic Complex Equations of First Order
1.2 Boundary Value Problems for Elliptic Complex Equations with
Nonsmooth Boundary
1.3 Nonlinear Riemann-Hilbert Problem for Elliptic Complex Equations
in Multiply Connected Domains
1.4 The Riemann-Hilbert Problem for Quasilinear Degenerate Elliptic
Complex Equations of First Order
1.5 Discontinuous Riemann-Hilbert Problem for Quasilinear Degenerate
Elliptic Complex Equations of First Order
Chapter 2 Nonlinear Elliptic Equations of Second Order
2.1 Discontinuous Oblique Derivative Problem for Uniformly Elliptic
Complex Equations of Second Order
2.2 Poincare Boundary Value Problem for Nonlinear Elliptic Equations of
Second Order
2.3 General Oblique Derivative Problem for Nonlinear Elliptic Equations
of Second Order
2.4 Discontinuous Irregular Oblique Derivative Problem of Nonlinear
Elliptic Equations of Second Order
2.5 Boundary Value Problems for Nonlinear Degenerate Elliptic Equations
of Second Order
Chapter 3 Nonlinear Elliptic Systems of Equations
3.1 Boundary Value Problems for Uniformly Elliptic Systems of Second
Order Equations
3.2 Boundary Value Problems for Nonlinear Elliptic Systems of Second
Order Equations
3.3 Boundary Value Problems of Nonlinear Elliptic Systems of Several
First Order Complex Equations
3.4 Boundary Value Problems for Nonlinear Elliptic Systems with
Several Unknown Functions
3.5 Degenerate Elliptic Systems of Second Order with Several Unknown
Functions
3.6 Boundary Value Problems for Nonlinear Elliptic Complex Equations
of Fourth Order
Chapter 4 Nonlinear Parabolic Equations and Systems
4.1 Formulation and Inner Estimates of Solutions of Initial-Boundary
Value Problems for Nonlinear Parabolic Equations
4.2 Estimate of Solutions and Solvability of Dirichlet Problem
4.3 Initial-Oblique Derivative Problem for Nonlinear Parabolic
Equations
4.4 Initial-Irregular Oblique Derivative Problem for Nonlinear Parabolic
Equations
4.5 Initial-Boundary Value Problem for Nonlinear Parabolic Systems of
Equations
Chapter 5 Quasilinear Hyperbolic Equations and Systems
5.1 The Riemann-Hilbert Problem for Hyperbolic Complex Equations of
First Order
5.2 Oblique Derivative Problem for Uniformly Hyperbolic Equations of
Second Order
5.3 Oblique Derivative Problem for Quasilinear Degenerate Hyperbolic
Equations of Second Order
5.4 Cauchy Problem for Quasilinear Hyperbolic Equations with
Degenerate Rank 0
5.5 Darboux Type Problem for Degenerate Hyperbolic Systems of
Second Order Equations
Chapter 6 Quasilinear Equations of Mixed Type
6.1 The Riemann-Hilbert Problem for First Order Complex Equations of
Mixed Type with Degenerate Line
6.2 The Tricomi Problem for Second Order Quasilinear Equations of
Mixed Type with Parabolic Degeneracy
6.3 Frankl Type Problem for Second Order Quasilinear Degenerate
Equations of Mixed Type
6.4 Boundary Value Problems for Degenerate Equations of Mixed Type
in Multiply Connected Domains
6.5 Oblique Derivative Problem for Quasilinear Equations of Mixed Type
with Nonsmooth Degenerate Line
6.6 Oblique Derivative Problem for Second Order Quasilinear Systems
of Mixed Type with Parabolic Degeneracy
Chapter 7 Applications of Nonlinear Complex Analysis to Continuum Mechanics
7.1 Free Boundary Problems in Planar Filtration
7.2 Degenerate Elliptic Boundary Value Problem and Axisymmetric
Filtration
7.3 Some Free Boundary Problems in Planar Subsonic Flow
7.4 Free Boundary Problems for Cavity Flows in Gas Dynamics
7.5 Free Boundary Problems in Elastico-Plastic Mechanics
References
Chapter 1 Nonlinear Elliptic Complex Equations of First Order
1.1 Discontinuous Riemann-Hilbert Problem for Nonlinear Uniformly
Elliptic Complex Equations of First Order
1.2 Boundary Value Problems for Elliptic Complex Equations with
Nonsmooth Boundary
1.3 Nonlinear Riemann-Hilbert Problem for Elliptic Complex Equations
in Multiply Connected Domains
1.4 The Riemann-Hilbert Problem for Quasilinear Degenerate Elliptic
Complex Equations of First Order
1.5 Discontinuous Riemann-Hilbert Problem for Quasilinear Degenerate
Elliptic Complex Equations of First Order
Chapter 2 Nonlinear Elliptic Equations of Second Order
2.1 Discontinuous Oblique Derivative Problem for Uniformly Elliptic
Complex Equations of Second Order
2.2 Poincare Boundary Value Problem for Nonlinear Elliptic Equations of
Second Order
2.3 General Oblique Derivative Problem for Nonlinear Elliptic Equations
of Second Order
2.4 Discontinuous Irregular Oblique Derivative Problem of Nonlinear
Elliptic Equations of Second Order
2.5 Boundary Value Problems for Nonlinear Degenerate Elliptic Equations
of Second Order
Chapter 3 Nonlinear Elliptic Systems of Equations
3.1 Boundary Value Problems for Uniformly Elliptic Systems of Second
Order Equations
3.2 Boundary Value Problems for Nonlinear Elliptic Systems of Second
Order Equations
3.3 Boundary Value Problems of Nonlinear Elliptic Systems of Several
First Order Complex Equations
3.4 Boundary Value Problems for Nonlinear Elliptic Systems with
Several Unknown Functions
3.5 Degenerate Elliptic Systems of Second Order with Several Unknown
Functions
3.6 Boundary Value Problems for Nonlinear Elliptic Complex Equations
of Fourth Order
Chapter 4 Nonlinear Parabolic Equations and Systems
4.1 Formulation and Inner Estimates of Solutions of Initial-Boundary
Value Problems for Nonlinear Parabolic Equations
4.2 Estimate of Solutions and Solvability of Dirichlet Problem
4.3 Initial-Oblique Derivative Problem for Nonlinear Parabolic
Equations
4.4 Initial-Irregular Oblique Derivative Problem for Nonlinear Parabolic
Equations
4.5 Initial-Boundary Value Problem for Nonlinear Parabolic Systems of
Equations
Chapter 5 Quasilinear Hyperbolic Equations and Systems
5.1 The Riemann-Hilbert Problem for Hyperbolic Complex Equations of
First Order
5.2 Oblique Derivative Problem for Uniformly Hyperbolic Equations of
Second Order
5.3 Oblique Derivative Problem for Quasilinear Degenerate Hyperbolic
Equations of Second Order
5.4 Cauchy Problem for Quasilinear Hyperbolic Equations with
Degenerate Rank 0
5.5 Darboux Type Problem for Degenerate Hyperbolic Systems of
Second Order Equations
Chapter 6 Quasilinear Equations of Mixed Type
6.1 The Riemann-Hilbert Problem for First Order Complex Equations of
Mixed Type with Degenerate Line
6.2 The Tricomi Problem for Second Order Quasilinear Equations of
Mixed Type with Parabolic Degeneracy
6.3 Frankl Type Problem for Second Order Quasilinear Degenerate
Equations of Mixed Type
6.4 Boundary Value Problems for Degenerate Equations of Mixed Type
in Multiply Connected Domains
6.5 Oblique Derivative Problem for Quasilinear Equations of Mixed Type
with Nonsmooth Degenerate Line
6.6 Oblique Derivative Problem for Second Order Quasilinear Systems
of Mixed Type with Parabolic Degeneracy
Chapter 7 Applications of Nonlinear Complex Analysis to Continuum Mechanics
7.1 Free Boundary Problems in Planar Filtration
7.2 Degenerate Elliptic Boundary Value Problem and Axisymmetric
Filtration
7.3 Some Free Boundary Problems in Planar Subsonic Flow
7.4 Free Boundary Problems for Cavity Flows in Gas Dynamics
7.5 Free Boundary Problems in Elastico-Plastic Mechanics
References
