Evolution Inclusions and Variation Inequalities for Earth Data Processing I
Here, the authors present modern mathematical methods to solve problems of differential-operator inclusions and evolution variation inequalities which may occur in fields such as geophysics, aerohydrodynamics, or fluid dynamics. For the first time, they d
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Series Editors: David Y. Gao, Virginia Polytechnic Institute and State University Ray W. Ogden, University of Glasgow Romesh C. Batra, Virginia Polytechnic Institute and State University Advisory Board: Ivar Ekeland, University of British Columbia Tim Healey, Cornell University Kumbakonom Rajagopal, Texas A&M University ´ Tudor Ratiu, Ecole Polytechnique F´ed´erale David J. Steigmann, University of California, Berkeley
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Mikhail Z. Zgurovsky • Valery S. Mel’nik Pavlo O. Kasyanov
Evolution Inclusions and Variation Inequalities for Earth Data Processing I Operator Inclusions and Variation Inequalities for Earth Data Processing
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Dr. Mikhail Z. Zgurovsky Pavlo O. Kasyanov Valery S. Mel’nik National Technical University of Ukraine “Kyiv Polytechnic Institute” Institute for Applied System Analysis National Academy of Sciences of Ukraine 37, Peremogy Ave. 03056 Kyiv Ukraine [email protected]
ISSN 1571-8689 e-ISSN 1876-9896 ISBN 978-3-642-13836-2 e-ISBN 978-3-642-13837-9 DOI 10.1007/978-3-642-13837-9 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010936816 c Springer-Verlag Berlin Heidelberg 2011 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, reuse of illustrations, recitation, broadcasting, reproduction on microfilm 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. Violations are liable to prosecution under the German Copyright Law. 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. Cover design: deblik, Berlin Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
The necessity of taking into account non-linear effects, memory effects, sharpening conditions, semipenetration etc has arisen in recent years. It is caused by intensification of processes in applied chemistry, petrochemistry, transportation of energy carriers, physics, energetics, mechanics, economics and in other fields of technology and industry. When modeling such phenomena we are faced with nonlinear boundary value problems for partial differential equations with multivalued or discontinuous right-hand side, variational inequalities (evolutional as well as stationary), an evolutional problem on manifolds (either with or without boundary), paired equations, cascading systems etc. Interpreting a concept of derivative properly we can treat all these objects as operator or differential-operator inclusions in Banach spaces and study t
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