Amplitude equations for stochastic partial differential equations
Author(s)
Bibliographic Information
Amplitude equations for stochastic partial differential equations
（Interdisciplinary mathematical sciences, v. 3）
World Scientific, c2007
Available at / 11 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Note
Includes bibliographical references and index
Description and Table of Contents
Description
Rigorous error estimates for amplitude equations are well known for deterministic PDEs, and there is a large body of literature over the past two decades. However, there seems to be a lack of literature for stochastic equations, although the theory is being successfully used in the applied community, such as for convective instabilities, without reliable error estimates at hand. This book is the first step in closing this gap.The author provides details about the reduction of dynamics to more simpler equations via amplitude or modulation equations, which relies on the natural separation of time-scales present near a change of stability.For students, the book provides a lucid introduction to the subject highlighting the new tools necessary for stochastic equations, while serving as an excellent guide to recent research.
Table of Contents
- : Formal Derivation of Amplitude Equations
- Rigorous Results on Bounded Domains, SDEs as Amplitude Equations
- Applications: Approximation of Invariant Measures
- Pattern Formation Below Criticality
- Approximate Center Manifold
- Large Domains, SPDEs as Amplitude Equations.
by "Nielsen BookData"