Effective Dynamics of Stochastic Partial Differential Equations

ISBN-13: 9780128008829 / Angielski / Twarda / 2014 / 282 str.

Jinqiao Duan

Opis

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

Recenzje

"Graduate students as well as researchers who have a solid background in SPDEs and are interested in undertaking research in the direction of averaging or homogenization of SPDEs can start their adventure and journey from the book." --MathSciNet

Spis treści

1. Introduction2. Deterministic Partial Differential Equations3. Stochastic Tools in Hilbert Space4. Stochastic Partial Differential Equations 5. Stochastic Averaging Principles6. Slow Manifold Reduction7. Stochastic Homogenization

O autorze

Illinois Institute of Technology, Chicago IL