- 非线性自治动力系统的吸引子(英文版)
- - 作者：秦玉明//苏克勤
  - 出版社：科学
  - ISBN：9787030702500
  - 出版日期：2022/01/01
  - 页数：212
- 售价：51.2

内容大纲
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最新结果，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。
作者介绍
目录
Preface
CHAPTER 1  Preliminary
  1.1  Some Useful Inequalities
  1.2  Basic Theory of Infinite-Dimensional Dynamical Systems for Autonomous Nonlinear Evolutionary Equations
    1.2.1  Uniformly Compact Semigroups
    1.2.2  Weakly Compact Semigroups
    1.2.3  Q-Limit Compact Semigroups
    1.2.4  Asymptotically Compact Semigroups
    1.2.5  Asymptotically Smooth Semigroups
    1.2.6  Norm-to-Weak Continuous Semigroups
    1.2.7  Closed Operator Semigroups
  1.3  Basic Theory of Finite-Dimensional Attractors
    1.3.1  The Fractal Dimension of Global Attractors
    1.3.2  The Estimate on Fractal Dimension of Global Attractors
CHAPTER 2  Global Attractors for the Navier-Stokes-Voight Equations with Delay
  2.1  Global Wellposedness of Solutions
  2.2  Existence of Global Attractors
    2.2.1  Dissipation: Existence of Absorbing Sets
    2.2.2  Asymptotical Compactness and Existence of Attractor
  2.3  Bibliographic Comments
CHAPTER 3  Global Attractor and Its Upper Estimate on Fractal Dimension for the 2D Navier-Stokes-Voight Equations
  3.1  Global Existence of Solutions
  3.2  Existence of Global Attractors
    3.2.1  Existence of Absorbing Sets
    3.2.2  Some Compactness and the Existence of Global Attractors
  3.3  Upper Estimate on the Fractal Dimension of Global Attractors
  3.4  Bibliographic Comments
CHAPTER 4 Maximal Attractor for the Equations of One-Dimensional Compressible Polytropic Viscous Ideal Gas
  4.1 Our Problem
  4.2  Nonlinear Semigroup on
  4.3  Existence of an Absorbing Set in H(2)
  4.4  Existence of an Absorbing Set in H(2)β
  4.5  Proof of Theorem 4.2.1
  4.6  Bibliographic Comments
CHAPTER 5 Universal Attractors for a Nonlinear System of Compressible One-Dimensional Heat-Conducting Viscous Real Gas
  5.1  Main Results
  5.2  Nonlinear Co-Semigroup on Hi+(i=1,2)
  5.3  Existence of an Absorbing Set in H1δ
  5.4  Existence of an Absorbing Set in H2δ
  5.5  Proof of Theorem 5.1.1
  5.6  Bibliographic Comments
CHAPTER 6 Global Attractors for the Compressible Navier-Stokes Equations in Bounded Annular Domains
  6.1  Main Result
  6.2  Nonlinear Semigroup on
  6.3  Existence of an Absorbing Set in H(1)δ
  6.4  Existence of an Absorbing Set in H(2)δ
  6.5  Existence of an Absorbing Set in H(4)δ
  6.6  Bibliographic Comments
CHAPTER 7 Global Attractor for a Nonlinear Thermoviscoelastic System in Shape Memory Alloys
  7.1  Main Result

  7.2  An Absorbing Set Bδ in Hδ
  7.3  Compactness of the Orbit in Hδ
  7.4  Bibliographic Comments
CHAPTER 8 Global Attractors for Nonlinear Reaction-Diffusion Equations and the 2D Navier-Stokes Equations
  8.1  Global Attractor for Strong Solutions of Reaction-Diffusion Equations
    8.1.1  Existence of Solutions and Uniqueness
    8.1.2  Global Attractor for the Semigroup in Lp(Ω)
    8.1.3  Global Attractor of System in Lp(Ω) and H10(Ω)
  8.2  Global Attractors for the 2D Navier-Stokes Equations in H10(Ω)
CHAPTER 9 Global Attractors for an Incompressible Fluid Equation and a Wave Equation
  9.1  An Incompressible Fluid Equation
  9.2  A Wave Equation with Nonlinear Damping
    9.2.1  Wellposedness of Solutions
    9.2.2  Dissipativity
    9.2.3  Asymptotic Compactness and Existence of Global Attractor
References
Index

内容大纲

作者介绍

目录

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