Von Karman Evolution Equations Well-posedness and Long Time Dynamics
The main goal of this book is to discuss and present results on well-posedness, regularity and long-time behavior of non-linear dynamic plate (shell) models described by von Karman evolutions. While many of the results presented here are the outgrowth of
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IGOR CHUESHOV IRENA LASIECKA
Well-posedness and
Springer Monographs in Mathematics
Long-Time Dynamics
Springer Monographs in Mathematics
For other titles published in this series, go to http://www.springer.com/series/3733
Igor Chueshov · Irena Lasiecka
Von Karman Evolution Equations Well-Posedness and Long-Time Dynamics
123
Igor Chueshov Kharkov National University Department of Mechanics & Mathematics 61077 Kharkov Ukraine [email protected]
Irena Lasiecka University of Virginia Department of Mathematics Charlottesville, Virginia 22904 USA [email protected]
ISBN 978-0-387-87711-2 e-ISBN 978-0-387-87712-9 DOI 10.1007/978-0-387-87712-9 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010924290 Mathematics Subject Classification (2010): 35Q74; 37L05, 37L30, 74B20, 74K20, 74K25 c Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.1 Von Karman evolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.2 Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.3 Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.4 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.5 Brief outline of the book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 2 4 4 5 6
Part I Well-Posedness 1
Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Function spaces and embedding theorems . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Sobolev spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 Besov spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3 Lizorkin and real Hardy spaces . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.4 Vector-value
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