非线性双曲偏微分方程:英文 内容简介

作者科研实力雄厚，厚积薄发，写成不可多得的本领域经典学术专著，值得推广使用。

非线性双曲偏微分方程:英文 目录

Preface ...................................................................................................I Chapter 1 Introduction..................................................................... 1 1.1 Intention and Signi.cances ....................................................... 1 1.2 Basic Concepts ........................................................................ 7 1.3 Some Examples.......................................................................14 1.4 Preliminaries ..........................................................................18 Chapter 2 Cauchy Problem for Nonlinear Hyperbolic Systems in Diagonal Form ...........................................................25 2.1 The Single Nonlinear Hyperbolic Equation ...............................25 2.2 The Classical Solutions to Single Nonlinear Hyperbolic Equation ................................................................................322.3 Nonlinear Hyperbolic Equations in Diagonal Form....................40 Chapter 3 Singularities Caused by the Eigenvectors ....................50 3.1 Introduction ...........................................................................50 3.2 Completely Reducible Systems.................................................55 3.3 2-Step Completely Reducible Systems ......................................59 3.4 m(m> 2)-Step Completely Reducible Systems with Constant Eigenvalues ..............................................................67 3.5 Non-completely Reducible Systems ..........................................74 3.6 Examples ...............................................................................76 Chapter 4 Hyperbolic Geometric Flow on Riemannian Surfaces...........................................................................854.1 Introduction ...........................................................................85 4.2 Cauchy Problem for Hyperbolic Geometric Flow.......................87 4.3 Mixed Initial Boundary Value Problem for Hyperbolic Geometric Flow ......................................................................99 4.4 Dissipative Hyperbolic Geometric Flow .................................. 107 4.5 Explicit Solutions..................................................................119 4.6 Radial Solutions to Hyperbolic Geometric Flow ...................... 124 Chapter 5 Life-Span of Classical Solutions to Hyperbolic Geometric Flow in Two Space Variables with Slow Decay Initial Data .............................................. 127 5.1 Intention and Signi.cances .................................................... 127 5.2 Some Useful Lemmas ............................................................ 130 5.3 Lower Bound of Life-Span ..................................................... 143 Chapter 6 Nonlinear Hyperbolic Systems with Relaxation ...... 153 6.1 Introduction ......................................................................... 153 6.2 Global Classical Solutions...................................................... 155 6.3 Applications .........................................................................162 6.4 Convergence of Approximate Solutions...................................165 Chapter 7 Applications.................................................................. 175 7.1 One Dimensional Hydromagnetic Dynamics............................175 7.2 Fluid Flow on a Pipe ............................................................ 187 7.3 Heat Conduction with Finite of Propagation .......................... 189 7.4 A Nonlinear Systems in Viscoelasticity...................................191 Bibliography ...................................................................................... 202 Index .................................................................................................. 209

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