Application of Abstract Differential Equations to Some Mechanical Problems (Mathematics and Its Applications (Kluwer ))

個数:

Application of Abstract Differential Equations to Some Mechanical Problems (Mathematics and Its Applications (Kluwer ))

  • 提携先の海外書籍取次会社に在庫がございます。通常3週間で発送いたします。
    重要ご説明事項
    1. 納期遅延や、ご入手不能となる場合が若干ございます。
    2. 複数冊ご注文の場合、分割発送となる場合がございます。
    3. 美品のご指定は承りかねます。
  • 【入荷遅延について】
    世界情勢の影響により、海外からお取り寄せとなる洋書・洋古書の入荷が、表示している標準的な納期よりも遅延する場合がございます。
    おそれいりますが、あらかじめご了承くださいますようお願い申し上げます。
  • ◆画像の表紙や帯等は実物とは異なる場合があります。
  • ◆ウェブストアでの洋書販売価格は、弊社店舗等での販売価格とは異なります。
    また、洋書販売価格は、ご注文確定時点での日本円価格となります。
    ご注文確定後に、同じ洋書の販売価格が変動しても、それは反映されません。
  • 製本 Hardcover:ハードカバー版/ページ数 209 p.
  • 言語 ENG
  • 商品コード 9781402014512
  • DDC分類 515.724

Full Description

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].

Contents

- Preface.
- Introduction. 1. Laplace problem in a strip. 2. Laplace problem in a sector. 3. Presentation of the different chapters.
- 1: General notions, definitions and results. 1. Introduction. 2. General notions from functional analysis. 3. Vector-value functions of Banach spaces. 4. Semigroup of linear bounded operators in a Banach space. 5. Differential-operator equations and fold completeness. 6. Isomorphism and coerciveness. 7. Interpolation of spaces. 8. Useful theorems.
- 2: Thermal conduction in a half-strip and a sector. 1. Asymptotic expansion for the thermal conduction in a plate. 2. Completeness of a system of root functions for the thermal conduction in a half-strip and a sector with smooth coefficients. 3. Completeness of a system of root functions for the thermal conduction in a half-strip with piecewise smooth coefficients.
- 3: Elasticity problems in a half-strip. 1. Asymptotic expansion for the elasticity in a plate. 2. Completeness of a system of root functions for elasticity problems in a half-strip. 3. Thermoelasticity systems in bounded domains with non-smooth boundaries.
- 4: Completeness of elementary solutions of problems for second and fourth orders elliptic equations in semi-infinite tube domains. 1. Abstract results for second order elliptic equations. 2. Boundary value problems for second order elliptic equations. 3. Boundary value problems for fourth order elliptic equations.
- 5: Basis property of elementary solutions for second order elliptic equations with a selfadjoint operator coefficient. 1. Abstract results for second order elliptic equations with a selfadjoint operator coefficient. 2. Boundary value problems for second order elliptic equations.
- Problems. References. List of notations.
- Subject index. Author index.