Mathematical Problems in Elasticity and Homogenization

O.A. Oleinik, A.S. Shamaev and G.A. Yosifian (Eds.)0444884416, 9780444884411, 9780080875477

This monograph is based on research undertaken by the authors during the last ten years. The main part of the work deals with homogenization problems in elasticity as well as some mathematical problems related to composite and perforated elastic materials. This study of processes in strongly non-homogeneous media brings forth a large number of purely mathematical problems which are very important for applications. Although the methods suggested deal with stationary problems, some of them can be extended to non-stationary equations. With the exception of some well-known facts from functional analysis and the theory of partial differential equations, all results in this book are given detailed mathematical proof.
It is expected that the results and methods presented in this book will promote further investigation of mathematical models for processes in composite and perforated media, heat-transfer, energy transfer by radiation, processes of diffusion and filtration in porous media, and that they will stimulate research in other problems of mathematical physics and the theory of partial differential equations.

---

Table of contents :
Content:
Editors
Page ii

Edited by
Page iii

Copyright page
Page iv

Preface
Pages xi-xiii

Chapter I Some Mathematical Problems of the Theory of Elasticity
Pages 1-117

Chapter II Homogenization of the System of Linear Elasticity. Composites and Perforated Materials
Pages 119-261

Chapter III Spectral Problems
Pages 263-381

References
Pages 383-398