这是本全英文版本。本书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。

本书主要研究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。

本书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。

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