拟线性双曲型方程组Cauchy问题

出版时间：2006-1  出版社：黄河水利出版社  作者：刘法贵  页数：181  

内容概要

　　《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。

书籍目录

PrefaceChapter 1 Introduction1.1 Intention and Significances1.2 Basic Concepts1.3 PreliminariesChapter 2 The Single Quasilinear Hyperbolic Systems2.1 Homogeneous Quasilinear Hyperbolic Equation2.2 Inhomogeneous Quasilinear Hyperbolic Equation2.3 Periodic Solutions to Quasilinear Hyperbolic Equation2.4 Quasilinear Hyperbolic Equation with Higher DissipationChapter 3 Quasilinear Hyperbolic Systems in Diagonal Form3.1 Reducible Quasilinear Hyperbolic Systems3.2 Life Span of C1 Solutions to Reducible Quasilinear HyperbolicSystems3.3 Quasilinear Hyperbolic Systems in Diagonal Form3.4 Hyperbolic Systems with Discontinuous CoefficientsChapter 4 Discontinuous Initial Value Problem for Quasilinear HyperbolicSystems4.1 Discontinuous Initial Value Problem4.2 A Uniform a Priori Estimate4.3 Typical Boundary Value Problem4.4 Typical Free Boundary Value Problem on a Fan-shaped Domain.4.5 Discontinuous Initial Value Problem for Inentropic Folwwith Dissipative Term4.6 Typical Free Value Problem for Quasilinear Hyperbolic Systemswith DissipationChapter 5 Singularities Caused by the Eigenvectors5.1 Introduction5.2 Completely Reducible Systems5.3 2-Step Completely Reducible Systems with Constant Eigenvalues.5.4 m （m > 2）-Step Completely Reducible Systems with ConstantEigenvalues5.5 Non-Completely Reducible Systems5.6 ExamplesChapter 6 Quasilinear Hyperbolic Systems with Dissipative Term6.1 Introduction6.2 Reducible Qualinear Hyperbolic Systems with Dissipation6.3 Formation of Singularities6.4 ApplicationsChapter 7 Quasilinear Hyperbolic Systems with Relaxation7.1 Introduction7.2 Global Classical Solutions7.3 Applications7.4 Convergence of Approximate SolutionsChapter 8 Cauchy Problem for Quasilinear Hyperbolic Systems in LinearlyDegenerate Type8.1 Introduction8.2 Preliminaries8.3 Proof of Theorem 8.2.18.4 ApplicationsBibliography