Application of Abstract Differential Equations to Some Mechanical Problems / Edition 1

Application of Abstract Differential Equations to Some Mechanical Problems / Edition 1

by I. Titeux, Yakov Yakubov
     
 

ISBN-10: 1402014511

ISBN-13: 9781402014512

Pub. Date: 08/31/2003

Publisher: Springer Netherlands

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

Overview

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.

Product Details

ISBN-13:
9781402014512
Publisher:
Springer Netherlands
Publication date:
08/31/2003
Series:
Mathematics and Its Applications (closed) Series, #558
Edition description:
2003
Pages:
209
Product dimensions:
6.69(w) x 9.61(h) x 0.36(d)

Table of 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.

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