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Application of Abstract Differential Equations to Some Mechanical Problems

  • Book
  • © 2003

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Authors:
  1. Isabelle Titeux

    1. Reims University, Reims, France

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  2. Yakov Yakubov

    1. Tel-Aviv University, Tel-Aviv, Israel

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Mathematics and Its Applications (MAIA, volume 558)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xxii
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  2. General notions, definitions, and results

    • Isabelle Titeux, Yakov Yakubov
    Pages 1-39

  3. Thermal conduction in a half-strip and a sector

    • Isabelle Titeux, Yakov Yakubov
    Pages 41-81

  4. Elasticity problems in a half-strip

    • Isabelle Titeux, Yakov Yakubov
    Pages 83-135

  5. Completeness of elementary solutions of problems for second and fourth orders elliptic equations in semi-infinite tube domains

    • Isabelle Titeux, Yakov Yakubov
    Pages 137-179

  6. Basis property of elementary solutions for second order elliptic equations in semi-infinite tube domains

    • Isabelle Titeux, Yakov Yakubov
    Pages 181-194

  7. Back Matter

    Pages 195-209
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Keywords

About this book

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].

Authors and Affiliations

  • Reims University, Reims, France

    Isabelle Titeux

  • Tel-Aviv University, Tel-Aviv, Israel

    Yakov Yakubov

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