Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes
The book presents variational methods combined with boundary integral equation techniques in application to a model of dynamic bending of plates with transverse shear deformation. The emphasis is on the rigorous mathematical investigation of the model, wh
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Igor Chudinovich
Christian Constanda
Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes
Igor Chudinovich, MS, PhD, DSc Professor of Mathematics, Faculty of Mechanical, Electrical, and Electronic Engineering The University of Guanajuato, Salamanca, GTO, Mexico Christian Constanda, MS, PhD, DSc Charles W. Oliphant Professor of Mathematical Sciences, The University of Tulsa 600 South College Avenue, Tulsa, Oklahoma 74104, USA
British Library Cataloguing in Publication Data Chudinovich, Igor Variational and potential methods for a class of linear hyperbolic evolutionary processes. – (Springer monographs in mathematics) 1. Plates (Engineering) – Mathematical models 2. Boundary element methods 3. Differential equations, Hyperbolic 4. Differential equations, Linear I. Title II. Constanda, C. (Christian) 515.3′535 ISBN 1852338881 Library of Congress Cataloging-in-Publication Data CIP data available.
Mathematics Subject Classification (2000): 35C15; 35D05; 35E05; 35L15; 35L20; 35Q72; 45F15; 74H20; 74H25; 74K20 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. Springer Monographs in Mathematics ISSN 1439-7382 ISBN 1-85233-888-1 Springer is a part of Springer Science+Business Media springeronline.com © Springer-Verlag London Limited 2005 Printed in the United States of America The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express of implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Typesetting: Camera-ready by the authors 12/3830-543210 Printer on acid-free paper SPIN 10991749
For Olga and Lia and the younger generation Genia and Dan
Preface
Variational and boundary integral equation techniques are two of the most useful methods for solving time-dependent problems described by systems of equations of the form ∂2u = Au, ∂t2 where u = u(x, t) is a vector-valued function, x is a point in a domain in R2 or R3 , and A is a linear elliptic differential operator. To facilitate a better understanding of these two types of methods, below we propose to illustrate their mechanisms in action on a specific mathematical model rather than in a more impersonal abstract setting. For this purpose, we have chosen the hyperbolic system of partial differential equations governing the n
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