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Application of Abstract Differential Equations to Some Mechanical Problems 🔍
Isabelle Titeux, Yakov Yakubov (auth.) Springer Netherlands : Imprint : Springer, Mathematics and Its Applications 558, 1, 2003
英语 [en] · PDF · 7.2MB · 2003 · 📘 非小说类图书 · 🚀/lgli/lgrs/nexusstc/zlib · Save
描述
PREFACE The theory of differential-operator equations has been described in various monographs, but the initial physical problem which leads to these equations is often hidden. When the physical problem is studied, the mathematical proofs are either not given or are quickly explained. In this book, we give a systematic treatment of the partial differential equations which arise in elastostatic problems. In particular, we study problems which are obtained from asymptotic expansion with two scales. Here the methods of operator pencils and differential-operator equations are used. This book is intended for scientists and graduate students in Functional Analy sis, Differential Equations, Equations of Mathematical Physics, and related topics. It would undoubtedly be very useful for mechanics and theoretical physicists. We would like to thank Professors S. Yakubov and S. Kamin for helpfull dis cussions of some parts of the book. The work on the book was also partially supported by the European Community Program RTN-HPRN-CT-2002-00274. xiii INTRODUCTION In first two sections of the introduction, a classical mathematical problem will be exposed: the Laplace problem. The domain of definition will be, on the first time, an infinite strip and on the second time, a sector. To solve this problem, a well known separation of variables method will be used. In this way, the structure of the solution can be explicitly found. For more details about the separation of variables method exposed in this part, the reader can refer to, for example, the book by D. Leguillon and E. Sanchez-Palencia [LS].
Erscheinungsdatum: 30.09.2012
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lgrsnf/A:\compressed\10.1007%2F978-94-007-1080-1.pdf
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nexusstc/Application of Abstract Differential Equations to Some Mechanical Problems/939f9645ec55f325e6d015b9732a3173.pdf
备用文件名
zlib/Mathematics/Isabelle Titeux, Yakov Yakubov (auth.)/Application of Abstract Differential Equations to Some Mechanical Problems_2102184.pdf
备选作者
by Isabelle Titeux, Yakov Yakubov
备用出版商
Springer Science + Business Media BV
备用出版商
Springer Nature
备用版本
Mathematics and Its Applications -- 558, Mathematics and Its Applications -- 558, Dordrecht, Netherlands, 2003
备用版本
Springer Nature, Dordrecht, 2003
备用版本
Netherlands, Netherlands
备用版本
1, 20121206
元数据中的注释
lg948295
元数据中的注释
{"edition":"1","isbns":["9400710801","9401037841","9789400710801","9789401037846"],"last_page":209,"publisher":"Springer Netherlands","series":"Mathematics and Its Applications 558"}
元数据中的注释
Online full text is restricted to subscribers.
Also available in print.
Mode of access: World Wide Web.
备用描述
The theory of differential operator equations has been described in various monographs. But the initial physical problem which leads to these equations is often hidden. When the physical problem is studied, the mathematical proofs are either not given or are quickly explained In this book, we give a systematic treatment of the differential equations with application to partial differential equations obtained from elastostatic problems. In particular, we study problems which are obtained from asymptotic expansion with two scales. We approximate and, when it is possible, expand the solution of problems by elementary solutions. This book is intended for scientists (mathematicians in the field of ordinary and partial differential equations, differential-operator equations; theoretical mechanics; theoretical physicists) and graduate students in Functional Analysis, Differential Equations, Equations of Mathematical Physics, and related topics.
备用描述
Front Matter....Pages i-xxii
General notions, definitions, and results....Pages 1-39
Thermal conduction in a half-strip and a sector....Pages 41-81
Elasticity problems in a half-strip....Pages 83-135
Completeness of elementary solutions of problems for second and fourth orders elliptic equations in semi-infinite tube domains....Pages 137-179
Basis property of elementary solutions for second order elliptic equations in semi-infinite tube domains....Pages 181-194
Back Matter....Pages 195-209
备用描述
Preface
Introduction. 1
1: General notions, definitions and results
2: Thermal conduction in a half-strip and a sector
3: Elasticity problems in a half-strip
4: Completeness of elementary solutions of problems for second and fourth orders elliptic equations in semi-infinite tube domains
5: Basis property of elementary solutions for second order elliptic equations with a selfadjoint operator coefficient
Subject index
Author index.
开源日期
2013-08-01
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