Global Well-posedness and Asymptotic Behavior of the Solutions to Non-classical Thermo(visco)elastic Models
This book presents recent findings on the global existence, the uniqueness and the large-time behavior of global solutions of thermo(vis)coelastic systems and related models arising in physics, mechanics and materials science such as thermoviscoelastic sy
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obal Well-posedness and Asymptotic Behavior of the Solutions to Non-classical Thermo(visco)elastic Models
Global Well-posedness and Asymptotic Behavior of the Solutions to Non-classical Thermo(visco)elastic Models
Yuming Qin Zhiyong Ma •
Global Well-posedness and Asymptotic Behavior of the Solutions to Non-classical Thermo(visco)elastic Models
123
Yuming Qin Department of Applied Mathematics Donghua University Shanghai China
ISBN 978-981-10-1713-1 DOI 10.1007/978-981-10-1714-8
Zhiyong Ma Shanghai Second Polytechnic University Shanghai China
ISBN 978-981-10-1714-8
(eBook)
Library of Congress Control Number: 2016943327 Mathematics Subject Classification (2010): 35B40, 80M35 © Springer Science+Business Media Singapore 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer Science+Business Media Singapore Pte Ltd.
To our parents To Yu Yin and Jia Qin To Zhangmi Huang
Preface
This book is designed to present recent results on some global well-posedness and asymptotic behavior of the solutions to non-classical thermo(visco)elastic models arising from physics, mechanics, and materials science such as thermoviscoelastic systems, thermoelastic systems of types II, III, and with second sound, Timoshenko-type system with past history. Some of the content of this book is based on the research carried out by the authors and their collaborators in recent years. Most of it has been previously published only in original papers, and some of the material has never been published until now. Therefore, the authors hope that the book will benefit both the interested beginner in the field and the expert. This book is divided into nine chapters. Chapter 1 is devoted to introducing some basic knowledge in modern analysis, some useful inequalities and basic theory of semigroups. In Chap. 2, we investigate one-dimensional nonlinear thermoelasticity with thermal memory and second
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