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ContentsPreface iCHAPTER 1Survey on Attractors in Time-Dependent Spaces 11.1 Time-Dependent Global Attractors 11.1.1 Oscillation Equations 11.1.2 Wave Equations 41.1.3 Reaction-Diffusion Equations 131.1.4 Berger Equations 181.1.5 Abstract Evolution Equations 191.2 Some Useful Definitions and Lemmas 29CHAPTER 2Time-Dependent Global Attractors for the Non-Classical Diffusion Equations with a Fading Memory 352.1 Introduction 352.2 Time-Dependent Global Attractors in A4t 382.2.1 Global Well-Posedness 382.2.2 Absorbing Sets 392.2.3 Time-Dependent Attractors 412.2.4 Regularity of Attractors 472.3 Bibliographic Comments 49CHAPTER 3Strong Attractors for the Non-Classical Diffusion Equation with a Fading Memory in Time-Dependent Spaces 513.1 Introduction 513.2 Existence and Uniqueness of Strong Solutions 543.3 Time-Dependent Global Attractors for Strong Solutions 583.3.1 Absorbing Sets in 583