《擬線性雙曲型方程組Cauchy問題》是黃河水利出版社出版的圖書，作者：劉法貴。
基本介紹
- 書名：擬線性雙曲型方程組Cauchy問題
- 出版社：黃河水利出版社
- 開本：16開
- 作者：劉法貴
- 頁數：181頁
- ISBN：7807340207
內容簡介,圖書目錄,
內容簡介
這是本全英文版本。本書主要研究了一階擬線性雙曲型方程組Cauchy問題，介紹了一階擬線性雙曲型方程組的基本概念及研究經典解的基本方法。全書討論了單個擬線性雙曲型方程、可約化擬線性雙曲型方程組、擬線性雙曲型方程的耗散和張弛問題、由特徵向量引發的奇性和具線性退化特徵雙曲型方程組。該書可供高等院校數學專業本科生、研究生、教師、科研人員閱讀參考。
圖書目錄
Preface
Chapter 1 Introduction
1.1 Intention and Significances
1.2 Basic Concepts
1.3 Preliminaries
Chapter 2 The Single Quasilinear Hyperbolic Systems
2.1 Homogeneous Quasilinear Hyperbolic Equation
2.2 Inhomogeneous Quasilinear Hyperbolic Equation
2.3 Periodic Solutions to Quasilinear Hyperbolic Equation
2.4 Quasilinear Hyperbolic Equation with Higher Dissipation
Chapter 3 Quasilinear Hyperbolic Systems in Diagonal Form
3.1 Reducible Quasilinear Hyperbolic Systems
3.2 Life Span of C1 Solutions to Reducible Quasilinear Hyperbolic
Systems
3.3 Quasilinear Hyperbolic Systems in Diagonal Form
3.4 Hyperbolic Systems with Discontinuous Coefficients
Chapter 4 Discontinuous Initial Value Problem for Quasilinear Hyperbolic
Systems
4.1 Discontinuous Initial Value Problem
4.2 A Uniform a Priori Estimate
4.3 Typical Boundary Value Problem
4.4 Typical Free Boundary Value Problem on a Fan-shaped Domain.
4.5 Discontinuous Initial Value Problem for Inentropic Folw
with Dissipative Term
4.6 Typical Free Value Problem for Quasilinear Hyperbolic Systems
with Dissipation
Chapter 5 Singularities Caused by the Eigenvectors
5.1 Introduction
5.2 Completely Reducible Systems
5.3 2-Step Completely Reducible Systems with Constant Eigenvalues.
5.4 m (m > 2)-Step Completely Reducible Systems with Constant
Eigenvalues
5.5 Non-Completely Reducible Systems
5.6 Examples
Chapter 6 Quasilinear Hyperbolic Systems with Dissipative Term
6.1 Introduction
6.2 Reducible Qualinear Hyperbolic Systems with Dissipation
6.3 Formation of Singularities
6.4 Applications
Chapter 7 Quasilinear Hyperbolic Systems with Relaxation
7.1 Introduction
7.2 Global Classical Solutions
7.3 Applications
7.4 Convergence of Approximate Solutions
Chapter 8 Cauchy Problem for Quasilinear Hyperbolic Systems in Linearly
Degenerate Type
8.1 Introduction
8.2 Preliminaries
8.3 Proof of Theorem 8.2.1
8.4 Applications
Bibliography
Chapter 1 Introduction
1.1 Intention and Significances
1.2 Basic Concepts
1.3 Preliminaries
Chapter 2 The Single Quasilinear Hyperbolic Systems
2.1 Homogeneous Quasilinear Hyperbolic Equation
2.2 Inhomogeneous Quasilinear Hyperbolic Equation
2.3 Periodic Solutions to Quasilinear Hyperbolic Equation
2.4 Quasilinear Hyperbolic Equation with Higher Dissipation
Chapter 3 Quasilinear Hyperbolic Systems in Diagonal Form
3.1 Reducible Quasilinear Hyperbolic Systems
3.2 Life Span of C1 Solutions to Reducible Quasilinear Hyperbolic
Systems
3.3 Quasilinear Hyperbolic Systems in Diagonal Form
3.4 Hyperbolic Systems with Discontinuous Coefficients
Chapter 4 Discontinuous Initial Value Problem for Quasilinear Hyperbolic
Systems
4.1 Discontinuous Initial Value Problem
4.2 A Uniform a Priori Estimate
4.3 Typical Boundary Value Problem
4.4 Typical Free Boundary Value Problem on a Fan-shaped Domain.
4.5 Discontinuous Initial Value Problem for Inentropic Folw
with Dissipative Term
4.6 Typical Free Value Problem for Quasilinear Hyperbolic Systems
with Dissipation
Chapter 5 Singularities Caused by the Eigenvectors
5.1 Introduction
5.2 Completely Reducible Systems
5.3 2-Step Completely Reducible Systems with Constant Eigenvalues.
5.4 m (m > 2)-Step Completely Reducible Systems with Constant
Eigenvalues
5.5 Non-Completely Reducible Systems
5.6 Examples
Chapter 6 Quasilinear Hyperbolic Systems with Dissipative Term
6.1 Introduction
6.2 Reducible Qualinear Hyperbolic Systems with Dissipation
6.3 Formation of Singularities
6.4 Applications
Chapter 7 Quasilinear Hyperbolic Systems with Relaxation
7.1 Introduction
7.2 Global Classical Solutions
7.3 Applications
7.4 Convergence of Approximate Solutions
Chapter 8 Cauchy Problem for Quasilinear Hyperbolic Systems in Linearly
Degenerate Type
8.1 Introduction
8.2 Preliminaries
8.3 Proof of Theorem 8.2.1
8.4 Applications
Bibliography
