Some Applications to Models from Physics and Engineering
A vast number of physical and engineering models can be shown to give rise to equations involving an operator of the form $$\displaystyle \partial _{0}M_{0}+M_{1}+A $$ where A is a skew-selfadjoint operator of the form $$\displaystyle A=\begin {pmatrix} 0
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Rainer Picard · Des McGhee Sascha Trostorff · Marcus Waurick
A Primer
for a Secret
Shortcut to PDEs
of Mathematical Physics
Frontiers in Mathematics
Advisory Board Leonid Bunimovich (Georgia Institute of Technology, Atlanta) William Y. C. Chen (Nankai University, Tianjin) Benoît Perthame (Sorbonne Université, Paris) Laurent Saloff-Coste (Cornell University, Ithaca) Igor Shparlinski (The University of New South Wales, Sydney) Wolfgang Sprößig (TU Bergakademie Freiberg) Cédric Villani (Institut Henri Poincaré, Paris)
More information about this series at http://www.springer.com/series/5388
Rainer Picard • Des McGhee • Sascha Trostorff • Marcus Waurick
A Primer for a Secret Shortcut to PDEs of Mathematical Physics
Rainer Picard Institut f¨ur Analysis TU Dresden Dresden, Germany
Des McGhee Department of Mathematics and Statistics University of Strathclyde Glasgow, UK
Sascha Trostorff Mathematisches Seminar Christian-Albrechts-Universit¨at zu Kiel Kiel, Germany
Marcus Waurick Department of Mathematics and Statistics University of Strathclyde Glasgow, UK
ISSN 1660-8046 ISSN 1660-8054 (electronic) Frontiers in Mathematics ISBN 978-3-030-47332-7 ISBN 978-3-030-47333-4 (eBook) https://doi.org/10.1007/978-3-030-47333-4 Mathematics Subject Classification: 35F, 35-01 © Springer Nature Switzerland AG 2020 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, expressed 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 book is published under the imprint Birkhäuser, www.birkhauser-science.com, by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Introduction
A typical entry point into the field of (linear) partial differential equations is to consider general polynomials P (∂) in ∂ := (∂0 , . . . , ∂n ) with (complex or real) matrix coefficients. Here ∂k denotes the partial derivative with respect to the variable in the position la
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