# Application of Abstract Differential Equations to Some Mechanical Problems

• Isabelle Titeux
• Yakov Yakubov Book

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

1. Front Matter
Pages i-xxii
2. Isabelle Titeux, Yakov Yakubov
Pages 1-39
3. Isabelle Titeux, Yakov Yakubov
Pages 41-81
4. Isabelle Titeux, Yakov Yakubov
Pages 83-135
5. Isabelle Titeux, Yakov Yakubov
Pages 137-179
6. Isabelle Titeux, Yakov Yakubov
Pages 181-194
7. Back Matter
Pages 195-209

### Introduction

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].

### Keywords

Banach space Boundary value problem functional analysis mechanics partial differential equation thermoelasticity

#### Authors and affiliations

• Isabelle Titeux
• 1
• Yakov Yakubov
• 2
1. 1.Reims UniversityReimsFrance
2. 2.Tel-Aviv UniversityTel-AvivIsrael

### Bibliographic information

• DOI https://doi.org/10.1007/978-94-007-1080-1 