书籍详情
Nonlinear hyperbolic partial differential equations
作者：王玉柱、刘法贵
出版社：清华大学出版社
出版时间：2016-12-01
ISBN：9787302453765
定价：¥36.00
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内容简介
领域经典学术专著
作者简介
刘法贵，教授，理学博士，华北水利水电大学教务处处长。硕士生导师。河南省数学学会理事，郑州市数学学会理事。河南省学术技术带头人，河南省优秀中青年骨干教师，省级重点学科带头人，河南省“555”省级人选。从事拟线性双曲偏微分方程的研究，在国内外重要学术期刊上发表论文50余篇。
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 ................................................................................32
2.3 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...........................................................................85
4.1 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
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 ................................................................................32
2.3 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...........................................................................85
4.1 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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