Initial Boundary Value Problems in Mathematical Physics
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Initi al Bou nda ry Valu e Prob lem s in Mat hem atic al Physics Rolf leis Universit y of Bonn Federal Republic of Germany
Springer Fachmedien Wiesbaden GmbH
Copyright~·' Copyright © 1986 by Springer Fachmedien Wiesbaden
Originally published by B.G. Teubner, Stuttgart in 1986
All rights reserved. No part of this book may be reproduced by any means, nor transmitted, nor translated into a machine language without the written permission of the publisher. CIP-Kurztitelaufnahme der Deutschsn Bibliothsk: Leis, Rolf: Initial boundary value problems in mathematical physics/Rolf Leis. ISBN 978-3-519-02102-5 DOI 10.1007/978-3-663-10649-4
ISBN 978-3-663-10649-4 (eBook)
Library of Congress Cataloging-in-Publication Data. Leis, Rolf. Initial boundary value problems in mathematical physics "Lectures ... given at the University of Bonn in the academic year 1983/4 and in part at the University of Strathclyde, Glasgow"-Pref. Bibliography: p. 000 Includes indexes. 1. Initial value problems--Addresses, essays, lectures. 2. Boundary value problems--Addresses, essays, lectures. I. Title. QA378.L45 1986 515.3'5 85-12473 ISBN 978-3-519-02102-5 British Library Cataloguing in Publication Data: Leis, R. Initial boundary value problems in mathematical physics 1. Initial value problems I. Title 515.3"5 QA378
Typeset by Macmillan India Ltd., Bangalore 25.
Preface The lectures presented in this book were given at the University of Bonn in the academic year 1983/4 and in part at the University of Strathclyde, Glasgow. Their aim was to introduce graduate students of both mathematics and physics to the timedependent theory of linear equations of mathematical physics and to classical scattering theory. Using Hilbert space methods, the theory was developed so that the asymptotic behaviour of the solutions for large t could be discussed. The presentation of the theory is made using equations that are of particular interest for the mathematician and the physicist. The wave equation is considered, as are firstorder systems of linear acoustics and electromagnetism. This is followed by a discussion of a Schrodinger equation with a Coulomb potential, the equations of linear elasticity, the plate equation, and the equations of thermoelasticity. The reader is assumed to have a basic knowledge of functional analysis. However, for convenience, the required background is presented in the second chapter. Because of the breadth of the subject, restrictions have to be made. For instance, the treatment of boundary value problems is confined to bounded and exterior domains (domains with bounded complement). Half spaces, for example, will not be discussed. Furthermore, when dealing with exterior boundary value problems, we assume the existence of a sufficiently large ball outside of which the medium is homogeneous and usually isotropic. The lectures are primarily concerned with vibrations; damping terms are only occasionally considered. The selection of the material follows personal interests and tastes. Only a few historical remarks are included, and alt
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