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Effective dynamics of stochastic partial differential equations / Jinqiao Duan and Wei Wang.

By: Contributor(s): Material type: TextTextSeries: Elsevier insightsPublication details: Amsterdam : Elsevier, 2014.Description: xi, 270 p. ; 24 cmISBN:
  • 9780128008829 (hardback)
Subject(s): DDC classification:
  • 515.353 23 D812
Contents:
1. Introduction-- 2. Deterministic partial differential equations-- 3. Stochastic calculus in Hilbert space-- 4. Stochastic partial differential equations-- 5. Stochastic averaging principles-- 6. Slow manifold reduction-- 7. Stochastic homogenization-- Hints and solutions-- Notations-- References.
Summary: 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.
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Includes bibligraphical references (pages 257-270).

1. Introduction--
2. Deterministic partial differential equations--
3. Stochastic calculus in Hilbert space--
4. Stochastic partial differential equations--
5. Stochastic averaging principles--
6. Slow manifold reduction--
7. Stochastic homogenization--

Hints and solutions--
Notations--
References.

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.

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