Effective Dynamics of Stochastic Partial Differential Equations

✍ Scribed by Jinqiao Duan and Wei Wang (Auth.)

• Publisher: Elsevier
• Year: 2014
• Tongue: English
• Leaves: 272
• Series: Elsevier Insights
• Edition: 1
• Category: Library

✦ Synopsis

Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations.

The authors' experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers by providing an accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Each chapter also includes exercises and problems to enhance comprehension.

• New techniques for extracting effective dynamics of infinite dimensional dynamical systems under uncertainty
• Accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations
• Solutions or hints to all Exercises

✦ Table of Contents

Content:
Effective Dynamics of Stochastic Partial Differential Equations, Page i
Effective Dynamics of Stochastic Partial Differential Equations, Page iii
Copyright, Page iv
Dedication, Page v
Preface, Pages ix-xi
Chapter 1 - Introduction, Pages 1-6
Chapter 2 - Deterministic Partial Differential Equations, Pages 7-20
Chapter 3 - Stochastic Calculus in Hilbert Space, Pages 21-47
Chapter 4 - Stochastic Partial Differential Equations, Pages 49-91
Chapter 5 - Stochastic Averaging Principles, Pages 93-143
Chapter 6 - Slow Manifold Reduction, Pages 145-185
Chapter 7 - Stochastic Homogenization, Pages 187-231
Hints and Solutions, Pages 233-254
Notations, Pages 255-256
References, Pages 257-270