Problems on Partial Differential Equations
This book covers a diverse range of topics in Mathematical Physics, linear and nonlinear PDEs. Though the text reflects the classical theory, the main emphasis is on introducing readers to the latest developments based on the notions of weak solutions and
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Maciej Borodzik Paweł Goldstein Piotr Rybka Anna Zatorska-Goldstein
Problems on Partial Differential Equations
Problem Books in Mathematics Series Editor: Peter Winkler Department of Mathematics Dartmouth College Hanover, NH 03755 USA
More information about this series at http://www.springer.com/series/714
Maciej Borodzik • Paweł Goldstein • Piotr Rybka • Anna Zatorska-Goldstein
Problems on Partial Differential Equations
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Maciej Borodzik The University of Warsaw Warsaw, Poland
Paweł Goldstein The University of Warsaw Warsaw, Poland
Piotr Rybka The University of Warsaw Warsaw, Poland
Anna Zatorska-Goldstein The University of Warsaw Warsaw, Poland
ISSN 0941-3502 ISSN 2197-8506 (electronic) Problem Books in Mathematics ISBN 978-3-030-14733-4 ISBN 978-3-030-14734-1 (eBook) https://doi.org/10.1007/978-3-030-14734-1 Library of Congress Control Number: 2019935542 Mathematics Subject Classification (2010): 35-01, 35A, 35J, 35K, 35L, 46-01, 46E, 46F © Springer Nature Switzerland AG 2019 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. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
In our teaching practice of presenting modern introductory courses on partial differential equations (PDEs for short), we have been facing a shortage of books with problems for independent study, which could be also used by lecturers. This book aims at bridging this gap. We use the term “modern introduction to PDEs” on purpose. This means that the emphasis is on the theory based on the Sobolev spaces and weak derivatives. We cover mostly the theory of linear equations of the elliptic, parabolic, and hyperbolic types. A few examples of nonlinear equations are included. We also consider elements of the classical theory of solutions to PDEs, e.g.,
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