Approximation of Stochastic Invariant Manifolds Stochastic Manifolds

This first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations. Th

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Mickaël D. Chekroun Honghu Liu Shouhong Wang

Approximation of Stochastic Invariant Manifolds Stochastic Manifolds for Nonlinear SPDEs I

SpringerBriefs in Mathematics Series editors Krishnaswami Alladi, Gainesville, USA Nicola Bellomo, Torino, Italy Michele Benzi, Atlanta, USA Tatsien Li, Shanghai, People’s Republic of China Matthias Neufang, Ottawa, Canada Otmar Scherzer, Vienna, Austria Dierk Schleicher, Bremen, Germany Benjamin Steinberg, New York, USA Yuri Tschinkel, New York, USA Loring W. Tu, Medford, USA G. George Yin, Detroit, USA Ping Zhang, Kalamazoo, USA

SpringerBriefs in Mathematics showcases expositions in all areas of mathematics and applied mathematics. Manuscripts presenting new results or a single new result in a classical field, new field, or an emerging topic, applications, or bridges between new results and already published works, are encouraged. The series is intended for mathematicians and applied mathematicians.

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Mickaël D. Chekroun Honghu Liu Shouhong Wang •

Approximation of Stochastic Invariant Manifolds Stochastic Manifolds for Nonlinear SPDEs I

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Shouhong Wang Indiana University Bloomington, IN USA

Mickaël D. Chekroun University of California Los Angeles, CA USA Honghu Liu University of California Los Angeles, CA USA

ISSN 2191-8198 SpringerBriefs in Mathematics ISBN 978-3-319-12495-7 DOI 10.1007/978-3-319-12496-4

ISSN 2191-8201 (electronic) ISBN 978-3-319-12496-4

(eBook)

Library of Congress Control Number: 2014956373 Mathematics Subject Classification: 37L65, 37D10, 37L25, 35B42, 37L10, 37L55, 60H15, 35R60, 34F05, 34G20, 37L05 Springer Cham Heidelberg New York Dordrecht London © The Author(s) 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)

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