- 非经典扩散方程和Kirchhoff波动方程的吸引子(英文版)
- - 作者：秦玉明//杨彬
  - 出版社：科学
  - ISBN：9787030780478
  - 出版日期：2024/01/01
  - 页数：253
- 售价：51.2

内容大纲
本书研究的内容为非经典扩散方程在时间依赖空间中的吸引子，受到时间依赖整体吸引子的一些研究成果的启发，我们首先研究了时间依赖整体吸引子和强吸引子的存在性，之后通过调整对时间依赖函数的假设，如重新设置其下界和单调性，得到了一些在时间依赖空间中关于拉回吸引子的存在性和正则性、以及拉回吸引子和整体吸引子的上半连续性的成果，它们都是新的尝试，并且通过这些模型的研究为在时间依赖空间中研究吸引子提供了一些新的思路和方法。此外，注意到时间依赖空间的范数中包含了时间依赖函数，因此很容易知道在此类空间中研究吸引子的存在性或其吸引子的其他性质要比在Sobolev空间中更为复杂和困难，例如在证明吸收集和渐近紧性时计算量会大大增加等。虽然计算和分析较为困难，但相空间范数中时间相关项的存在拓宽了以往的研究框架，使人们能够在更接近物理现实的模型中对解的长时间行为进行讨论，促进了对动力系统解的适定性的研究进程，具有重要意义。
作者介绍
目录
Preface
CHAPTER 1  Survey on Attractors in Time-Dependent Spaces
  1.1  Time-Dependent Global Attractors
    1.1.1  Oscillation Equations
    1.1.2  Wave Equations
    1.1.3  Reaction-Diffusion Equations
    1.1.4  Berger Equations
    1.1.5  Abstract Evolution Equations
  1.2  Some Useful Definitions and Lemmas
CHAPTER 2  Time-Dependent Global Attractors for the Non-Classical Diffusion Equations with a Fading Memory
  2.1  Introduction
  2.2  Time-Dependent Global Attractors in A4t
    2.2.1  Global Well-Posedness
    2.2.2  Absorbing Sets
    2.2.3  Time-Dependent Attractors
    2.2.4  Regularity of Attractors
  2.3  Bibliographic Comments
CHAPTER 3  Strong Attractors for the Non-Classical Diffusion Equation with a Fading Memory in Time-Dependent Spaces
  3.1  Introduction
  3.2  Existence and Uniqueness of Strong Solutions
  3.3  Time-Dependent Global Attractors for Strong Solutions
    3.3.1  Absorbing Sets in
    3.3.2  Time-Dependent Attractors
  3.4  Bibliographic Comments
CHAPTER 4  Long-Time Behavior of Solutions to the Non-Autonomous Non-Classical Diffusion Equations
  4.1  Introduction
  4.2  Global Well-Posedness of Solutions
  4.3  Existence of Pullback Attractors
    4.3.1  Pullback Dδ,Ht -Absorbing Set
    4.3.2  Pullback Dδ,Ht -Asymptotical Compactness
  4.4  Regularity of Attractors
  4.5  Bibliographic Comments
CHAPTER 5  Existence and Upper Semicontinuity of Attractors for Non-Autonomous Nonlocal Diffusion Equations
  5.1  Introduction
  5.2  Existence and Uniqueness of Solutions
  5.3  Existence of the Minimal Pullback P-Attractors
    5.3.1  Pullback 2)^-Absorbing Family
    5.3.2  Pullback Asymptotical Compactness
  5.4  Existence of Pullback Attractors * and Upper Semicontinuity of * and Global Attractor A
  5.5  Bibliographic Comments
CHAPTER 6  Pullback Attractors for Diffusion Equations with a Delay Function and a Nonlocal Diffusion Term in Time-Dependent
Spaces
  6.1  Introduction
  6.2  Existence and Uniqueness of Solutions
  6.3  Existence of Pullback Dη–Attractors
    6.3.1  Pullback Dη-Absorbing Family
    6.3.2  Pullback Dη- Asymptotical Compactness
  6.4  Regularity of Pullback Attractors
  6.5  Bibliographic Comments
CHAPTER 7  Existence and Regularity of Pullback Attractors for Non-Classical Diffusion Equations with a Delay Operator

  7.1  Introduction
  7.2  Existence and Uniqueness of Solutions
  7.3  Existence and Priori Estimates of Regularity for Pullback Attractors
  7.4  Regularity of Pullback Attractors
  7.5  Bibliographic Comments
CHAPTER 8  Survey on Attractors for Kirchhoff Wave Equations with Strong Dampings
  8.1  Attractors for Kirchhoff Wave Equations with Strong Dampings
CHAPTER 9  Existence, Regularity and Fractal Dimension of Global Attractors for a Kirchhoff Wave Equation with Strong Damping
and Memory
  9.1  Introduction
  9.2  Existence of Global Attractor A
  9.3  Regularity of Global Attractor A
      9.4 Fractal Dimension of Global Attractor A of Problem (9.1.1  ) withδ=
  9.5  Bibliographic Comments
Bibliography

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