Two-Scale Approach to Oscillatory Singularly Perturbed Transport Equations
This book presents the classical results of the two-scale convergence theory and explains – using several figures – why it works. It then shows how to use this theory to homogenize ordinary differential equations with oscillating coefficients as well as o
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Emmanuel Frénod
Two-Scale Approach to Oscillatory Singularly Perturbed Transport Equations
Lecture Notes in Mathematics Editors-in-Chief: Jean-Michel Morel, Cachan Bernard Teissier, Paris Advisory Board: Michel Brion, Grenoble Camillo De Lellis, Zurich Alessio Figalli, Zurich Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gábor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, New York Anna Wienhard, Heidelberg
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More information about this series at http://www.springer.com/series/304
Emmanuel Frénod
Two-Scale Approach to Oscillatory Singularly Perturbed Transport Equations
123
Emmanuel Frénod LMBA Université Bretagne Sud Vannes, France
ISSN 0075-8434 Lecture Notes in Mathematics ISBN 978-3-319-64667-1 DOI 10.1007/978-3-319-64668-8
ISSN 1617-9692 (electronic) ISBN 978-3-319-64668-8 (eBook)
Library of Congress Control Number: 2017950521 Mathematics Subject Classification (2010): 34Exx, 35L02, 65-xx, 82Dxx © Springer International Publishing AG 2017 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. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
Two-scale convergence is a homogenization tool. I have chosen to compile lecture notes on this topic for at least two reasons. First, two-scale convergence is certainly the homogenization tool that is easiest to handle. It can be conveniently used to tackle many phenomena involving oscillations or heterogeneities. With twoscale convergence, we can design effective models in a constructive way and without much analytical material. Besides, the effective models that are based on two-scale convergence do not generate (or explicitly contain) the oscillations or heterogeneities of the studied phenomena, but
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