Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics
The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of
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Ferruccio Colombini Daniele Del Santo David Lannes Editors
Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics
Springer INdAM Series Volume 17
Editor-in-Chief G. Patrizio Series Editors C. Canuto G. Coletti G. Gentili A. Malchiodi P. Marcellini E. Mezzetti G. Moscariello T. Ruggeri
More information about this series at http://www.springer.com/series/10283
Ferruccio Colombini • Daniele Del Santo • David Lannes Editors
Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics
123
Editors Ferruccio Colombini Dipartimento di Matematica UniversitJa di Pisa Pisa, Italy
Daniele Del Santo Dipartimento di Matematica e Geoscienze UniversitJa di Trieste Trieste, Italy
David Lannes Institut de Mathématiques de Bordeaux Université de Bordeaux - UMR5251 Talence, France
ISSN 2281-518X Springer INdAM Series ISBN 978-3-319-52041-4 DOI 10.1007/978-3-319-52042-1
ISSN 2281-5198 (electronic) ISBN 978-3-319-52042-1 (eBook)
Library of Congress Control Number: 2017939581 © 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
. . . , così come raia da l’un, se si conosce, il cinque e ’l sei; Par. XV, 56–57.
Preface
The present volume is a collection of papers with a strong focus on the study of nonlinear hyperbolic systems, and it addresses general theoretical issues such as symmetrizability, singularities, low regularity and dispersive perturbations. The past decade has been marked by important breakthroughs in the study of physical phenomena where the theory of hyperbolic systems plays a central role. We refer in particular to results in nonlinear optics, shock
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