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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

版次: 1

ISBN: 9787302453765

定价: 36.00

装帧: 其他

开本: 32开

纸张: 胶版纸

页数: 210页

字数: 265千字

分类: 自然科学

8人买过

领域经典学术专著刘法贵，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。 Preface...................................................................................................I

Chapter 1        Introduction.....................................................................1

1.1  Intentionand Signi.cances ....................................................... 1

1.2  BasicConcepts ........................................................................7

1.3  SomeExamples.......................................................................14

1.4  Preliminaries..........................................................................18

Chapter 2        CauchyProblem for Nonlinear Hyperbolic Systems in Diagonal Form...........................................................25

2.1  TheSingle Nonlinear Hyperbolic Equation ...............................25

2.2  TheClassical Solutions to Single Nonlinear Hyperbolic Equation ................................................................................32

2.3  NonlinearHyperbolic Equations in Diagonal Form....................40

Chapter 3        SingularitiesCaused by the Eigenvectors ....................50

3.1  Introduction...........................................................................50

3.2  CompletelyReducible Systems.................................................55

3.3  2-StepCompletely Reducible Systems ......................................59

3.4  m(m>2)-Step Completely Reducible Systems with Constant Eigenvalues..............................................................67

3.5  Non-completelyReducible Systems ..........................................74

3.6  Examples...............................................................................76

Chapter 4        HyperbolicGeometric Flow on RiemannianSurfaces...........................................................................85

4.1  Introduction...........................................................................85

4.2  CauchyProblem for Hyperbolic Geometric Flow.......................87

4.3  MixedInitial Boundary Value Problem for Hyperbolic Geometric Flow......................................................................99

4.4  DissipativeHyperbolic Geometric Flow .................................. 107

4.5  ExplicitSolutions..................................................................119

4.6  RadialSolutions to Hyperbolic Geometric Flow ...................... 124

Chapter 5        Life-Spanof Classical Solutions to Hyperbolic Geometric Flow in Two Space Variables withSlow Decay Initial Data .............................................. 127

5.1  Intentionand Signi.cances .................................................... 127

5.2  SomeUseful Lemmas ............................................................ 130

5.3  LowerBound of Life-Span ..................................................... 143

Chapter 6        NonlinearHyperbolic Systems with Relaxation ...... 153

6.1  Introduction......................................................................... 153

6.2  GlobalClassical Solutions...................................................... 155

6.3  Applications.........................................................................162

6.4  Convergenceof Approximate Solutions...................................165

Chapter 7        Applications..................................................................175

7.1 One Dimensional HydromagneticDynamics............................175

7.2 Fluid Flow on a Pipe............................................................ 187

7.3 Heat Conduction with Finite ofPropagation .......................... 189

7.4 A Nonlinear Systems inViscoelasticity...................................191

Bibliography......................................................................................202

Index..................................................................................................209
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  Intentionand Signi.cances ....................................................... 1

1.2  BasicConcepts ........................................................................7

1.3  SomeExamples.......................................................................14

1.4  Preliminaries..........................................................................18

Chapter 2        CauchyProblem for Nonlinear Hyperbolic Systems in Diagonal Form...........................................................25

2.1  TheSingle Nonlinear Hyperbolic Equation ...............................25

2.2  TheClassical Solutions to Single Nonlinear Hyperbolic Equation ................................................................................32

2.3  NonlinearHyperbolic Equations in Diagonal Form....................40

Chapter 3        SingularitiesCaused by the Eigenvectors ....................50

3.1  Introduction...........................................................................50

3.2  CompletelyReducible Systems.................................................55

3.3  2-StepCompletely Reducible Systems ......................................59

3.4  m(m>2)-Step Completely Reducible Systems with Constant Eigenvalues..............................................................67

3.5  Non-completelyReducible Systems ..........................................74

3.6  Examples...............................................................................76

Chapter 4        HyperbolicGeometric Flow on RiemannianSurfaces...........................................................................85

4.1  Introduction...........................................................................85

4.2  CauchyProblem for Hyperbolic Geometric Flow.......................87

4.3  MixedInitial Boundary Value Problem for Hyperbolic Geometric Flow......................................................................99

4.4  DissipativeHyperbolic Geometric Flow .................................. 107

4.5  ExplicitSolutions..................................................................119

4.6  RadialSolutions to Hyperbolic Geometric Flow ...................... 124

Chapter 5        Life-Spanof Classical Solutions to Hyperbolic Geometric Flow in Two Space Variables withSlow Decay Initial Data .............................................. 127

5.1  Intentionand Signi.cances .................................................... 127

5.2  SomeUseful Lemmas ............................................................ 130

5.3  LowerBound of Life-Span ..................................................... 143

Chapter 6        NonlinearHyperbolic Systems with Relaxation ...... 153

6.1  Introduction......................................................................... 153

6.2  GlobalClassical Solutions...................................................... 155

6.3  Applications.........................................................................162

6.4  Convergenceof Approximate Solutions...................................165

Chapter 7        Applications..................................................................175

7.1 One Dimensional HydromagneticDynamics............................175

7.2 Fluid Flow on a Pipe............................................................ 187

7.3 Heat Conduction with Finite ofPropagation .......................... 189

7.4 A Nonlinear Systems inViscoelasticity...................................191

Bibliography......................................................................................202

Index..................................................................................................209

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Nonlinear hyperbolic partial differential equations

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