Attractors for Non-Classical Diffusion Equations and Kirchhoff Wave Equations.

Format:

Book

Author/Creator:

Qin, Yuming.

Contributor:

Yang, Bin.

Series:

Current Natural Sciences Series

Language:

English

Physical Description:

1 online resource (268 pages)

Edition:

1st ed.

Place of Publication:

Les Ulis : EDP Sciences, 2024.

Summary:

This book presents the latest research on global well-posedness including asymptotic behavior of solutions to some non-classical diffusion equations with fading memories, nonlocal terms or delays in several time-dependent spaces. The results collected in this book have been established by the authors and their collaborators over recent years.This book has two distinguishing features. First, while there are many published works on non-classical diffusion equations in Sobolev spaces without time-dependent terms but few results in time-dependent spaces, this book fills this gap. Second, this book provides new results on the existence, regularity and upper semicontinuity of time-dependent global attractors, strong attractors, and pullback attractors in time-dependent spaces, as well as the ideas and methods for dealing with these problems that can be used in other related models.

Contents:

Frontmatter

Contents

Preface

CHAPTER 1 Survey on Attractors in Time-Dependent Spaces

CHAPTER 2 Time-Dependent Global Attractors for the Non-Classical Diffusion Equations with a Fading Memory

CHAPTER 3 Strong Attractors for the Non-Classical Diffusion Equation with a Fading Memory in Time-Dependent Spaces

CHAPTER 4 Long-Time Behavior of Solutions to the Non-Autonomous Non-Classical Diffusion Equations

CHAPTER 5 Existence and Upper Semicontinuity of Attractors for Non-Autonomous Nonlocal Diffusion Equations

CHAPTER 6 Pullback Attractors for Diffusion Equations with a Delay Function and a Nonlocal Diffusion Term in Time-Dependent Spaces

CHAPTER 7 Existence and Regularity of Pullback Attractors for Non-Classical Diffusion Equations with a Delay Operator

CHAPTER 8 Survey on 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

Bibliography

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9782759835393

2759835391

OCLC:

1459225124