非线性自治动力系统的吸引子
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作者秦玉明
出版社科学出版社
ISBN9787030702500
出版时间2024-03
装帧平装
开本16开
定价128元
货号29434630
上书时间2024-11-03
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作者简介
秦玉明，is full professor, head of Mathematics Department and director of Institute of Nonlinear Sciences of Donghua University. His research interests are global (local) wellposedness of solutions and infinite-dimensional dvnamical svstems for nonlinear evolutionarv equations including fluid equations such as Navier-Stokes equations, MHD, etc, and thermo(visco)elastic equations.
目录
Preface i
CHAPTER 1
Preliminary 1
1.1 Some Useful Inequalities 1
1.2 Basic Theory of Infinite-Dimensional Dynamical Systems for Autonomous Nonlinear Evolutionary Equations 10
1.2.1 Uniformly Compact Semigroups 10
1.2.2 Weakly Compact Semigroups 16
1.2.3 Q-Limit Compact Semigroups 17
1.2.4 Asymptotically Compact Semigroups 22
1.2.5 Asymptotically Smooth Semigroups 27
1.2.6 Norm-to-Weak Continuous Semigroups 28
1.2.7 Closed Operator Semigroups 30
1.3 Basic Theory of Finite-Dimensional Attractors 32
1.3.1 The Fractal Dimension of Global Attractors 32
1.3.2 The Estimate on Fractal Dimension of Global Attractors 33
CHAPTER 2 Global Attractors for the Navier-Stokes-Voight Equations with Delay 37
2.1 Global Wellposedness of Solutions 37
2.2 Existence of Global Attractors 43
2.2.1 Dissipation: Existence of Absorbing Sets 43
2.2.2 Asymptotical Compactness and Existence of Attractor 44
2.3 Bibliographic Comments 46
CHAPTER 3 Global Attractor and Its Upper Estimate on Fractal Dimension for the 2D Navier-Stokes-Voight Equations 47
3.1 Global Existence of Solutions 47
3.2 Existence of Global Attractors 55
3.2.1 Existence of Absorbing Sets 55
3.2.2 Some Compactness and the Existence of Global Attractors 56
3.3 Upper Estimate on the Fractal Dimension of Global Attractors 58
3.4 Bibliographic Comments 64
CHAPTER 4 Maximal Attractor for the Equations of One-Dimensional Compressible Polytropic Viscous Ideal Gas 67
41 Our Problem 67
4.2 Nonlinear Semigroup on 69
4.3 Existence of an Absorbing Set in 73
4.4 Existence of an Absorbing Set in 83
4.5 Proof of Theorem 4.2.1 86
4.6 Bibliographic Comments 88
CHAPTER 5 Universal Attractors for a Nonlinear System of Compressible One-Dimensional Heat-Conducting Viscous Real Gas 91
5.1 Main Results 91
5.2 Nonlinear Co-Semigroup on 95
5.3 Existence of an Absorbing Set in 97
5.4 Existence of an Absorbing Set in 106
5.5 Proof of Theorem 5.1.1 108
5.6 Bibliographic Comments 111
CHAPTER 6 Global Attractors for the Compressible Navier-Stokes Equations in Bounded Annular Domains 115
6.1 Main Result 115
6.2 Nonlinear Semigroup on 119
6.3 Existence of an Absorbing Set in 120
6.4 Existence of an Absorbing Set in 129
6.5 Existence of an Absorbing Set in 135
6.6 Bibliographic Comments 146
CHAPTER 7 Global Attractor for a Nonlinear Thermoviscoelastic System in Shape Memory Alloys 149
7.1 Main Result 149
7.2 An Absorbing Set in Hs 152
7.3 Compactness of the Orbit in Hs 165
7.4 Bibliographic Comments 173
CHAPTER 8 Global Attractors for Nonlinear Reaction-Diffusion Equations and the 2D Navier-Stokes Equations 175
8.1 Global Attractor for Strong Solutions of Reaction-Diffusion Equations 175
8.1.1 Existence of Solutions and Uniqueness 176
8.1.2 Global Attractor for the Semigroup in 176
8.1.3 Global Attractor of System in and 177
8.2 Global Attractors for the 2D Navier-Stokes Equations in 183
CHAPTER 9 Global Attractors for an Incompressible Fluid Equation and a Wave Equation 187
9.1 An Incompressible Fluid Equation 187
9.2 A Wave Equation with Nonlinear Damping 193
9.2.1 Wellposedness of Solutions 194
9.2.2 Dissipativity 196
9.2.3 Asymptotic Compactness and Existence of Global Attractor 200
References 203
Index 211
内容摘要
这本书是基于作者的讲义“非线性自治系统上的无穷维动力系统”，它的目的是系统整理和完善无穷维动力系统及其应用偏微分方程理论，特别是在流体力学方面。本书旨在介绍一些来自物理、流体力学和材料科学的自治非线性演化方程的**结果，如Navier-Stokes方程、Navier-Stokes-Voight系统、非线性热粘弹性系统，这本书的大部分内容都是基于作者近年来进行的研究，其中一些以前只在原始论文中发表，有些材料直到现在才发表。
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