Uncertainty Quantification for Hyperbolic and Kinetic Equations

This book explores recent advances in uncertainty quantification for hyperbolic, kinetic, and related problems. The contributions address a range of different aspects, including: polynomial chaos expansions, perturbation methods, multi-level Monte Carlo m

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Uncertainty Quantification for Hyperbolic and Kinetic Equations

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SEMA SIMAI Springer Series Series Editors: Luca Formaggia • Pablo Pedregal (Editor-in-Chief) Mats G. Larson • Tere Martínez-Seara Alonso • Carlos Parés • Lorenzo Pareschi • Andrea Tosin • Elena Vazquez • Jorge P. Zubelli • Paolo Zunino Volume 14

More information about this series at http://www.springer.com/series/10532

Shi Jin • Lorenzo Pareschi Editors

Uncertainty Quantification for Hyperbolic and Kinetic Equations

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Editors Shi Jin Department of Mathematics University of Wisconsin Madison, WI, USA

Lorenzo Pareschi Dipartimento di Matematica e Informatica UniversitJa degli Studi di Ferrara Ferrara, Italy

ISSN 2199-3041 ISSN 2199-305X (electronic) SEMA SIMAI Springer Series ISBN 978-3-319-67109-3 ISBN 978-3-319-67110-9 (eBook) https://doi.org/10.1007/978-3-319-67110-9 Library of Congress Control Number: 2018934713 © Springer International Publishing AG, part of Springer Nature 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 the registered company Springer International Publishing AG part of Springer Nature. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

Kinetic equations describe the probability density distribution of interacting particles, and often are also subject to the influence of external fields. The equations consist of transport, collision, source and forcing terms. Although kinetic equations, most notably the Boltzmann equation, are often derived from the mean-field approximations of the first principle Newton’s Second Law for N-particles by taking the N ! 1 limit, one can hardly exactly obtain the collision kernel, which is instead determined empirically, giving rise to uncertainty. More recently, kinetic equations have found applications in other fields, l