Materials with Memory Initial-Boundary Value Problems for Constituti
This book contributes to the mathematical theory of systems of differential equations consisting of the partial differential equations resulting from conservation of mass and momentum, and of constitutive equations with internal variables. The investigati
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1682
Lecture Notes in Mathematics Editors: A. Dold, Heidelberg F. Takens, Groningen
1682
Springer Berlin Heidelberg New York Barcelona Budapest Hong Kong London Milan Paris Santa Clara Singapore Tokyo
Hans-Dieter Alber
Materials with Memory Initial-Boundary Value Problems for Constitutive Equations with Internal Variables
Springer
Author Hans-Dieter Alber Fachbereich Mathematik Technische Universitat Darmstadt SchlossgartenstraBe 7 D-64289 Darmstadt, Germany e-mail: [email protected]
Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Alber, Hans-Dieter. Materials with memory: initial boundary value problems for constitutive equations with internal variables / Hans-Dieter Alber. Berlin; Heidelberg; New York; Barcelona; Bndapest ; Hong Kong; London; Milan; Paris; Santa Clara; Singapore; Tokyo: Springer,
1998
(Lecture notes in mathematics; 1682) ISBN 3-540-64066-5
Mathematics Subject Classification (1991): 35F25,35L45,35Q72, 73-02, 73E50, 73F15 ISSN 0075- 8434 ISBN 3-540-64066-5 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1998 Printed in Germany The use of general descriptive names, 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 protective laws and regulations and therefore free for general use. Typesetting: Camera-ready TEX output by the author SPIN: 10649759 46/3143-5432 IO - Printed on acid-free paper
Dedicated to Rolf Leis and to Jutta, Anne and Ina
Preface Continuum mechanics offers a rising number of fascinating problems to mathematical analysis, and the interest of mathematicians in these problems has been revived and is steadily growing. The reason behind this development is the computer. It makes more and more mathematical problems accessible to numerical treatment and thus opens an increasing number of regions to practical interest and application, which were formerly reserved to theoretical analysis. One might expect that this would diminish the interest in theoretical analysis. Fortunately, this is not the case. On the contrary, numerical studies call for a deeper analysis and thus open new fields in continuum mechanics to mathematical analysis. In a sense, by generating this renewed interest in continuum mechanics, the computer is leading mathematical analysis back to its origins in the studies of Newton
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