擬線性雙曲型方程組Cauchy問題

內(nèi)容概要

　　《擬線性雙曲型方程組Cauchy問題（英文版）》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(jīng)典解的基本方法。全書討論了單個(gè)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、由特征向量引發(fā)的奇性和具線性退化特征雙曲型方程組。該書可供高等院校數(shù)學(xué)專業(yè)本科生、研究生、教師、科研人員閱讀參考。

書籍目錄

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

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