拟线性双曲型方程组：Cauchy问题 英文版
作者：刘法贵 著
出版时间：2006年版
内容简介
《拟线性双曲型方程组Cauchy问题（英文版）》主要研究了一阶拟线性双曲型方程组Cauchy问题，介绍了一阶拟线性双曲型方程组的基本概念及研究经典解的基本方法。全书讨论了单个拟线性双曲型方程、可约化拟线性双曲型方程组、拟线性双曲型方程的耗散和张弛问题、由特征向量引发的奇性和具线性退化特征双曲型方程组。该书可供高等院校数学专业本科生、研究生、教师、科研人员阅读参考。
目录
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
