Oleinik / Shamaev / Yosifian Mathematical Problems in Elasticity and Homogenization

1. Auflage 2009
ISBN: 978-0-08-087523-1
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 499 Seiten

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.

Autoren/Hrsg.

Oleinik, O. A.

Shamaev, A. S.

Yosifian, G. A.

Inhaltsverzeichnis

1;Front Cover;1
2;Navier–Stokes Equations: Theory and Numerical Analysis;4
3;Copyright Page;5
4;Contents;8
5;Foreword;6
6;Chapter I The Steady-State Stokes Equations;12
6.1;Introduction;12
6.2;§1. Some function spaces;12
6.3;§2. Existence and uniqueness for the Stokes equations;31
6.4;§3. Discretization of the Stokes equations (I);50
6.5;§4. Discretization of the Stokes equations (II);76
6.6;§5. Numerical algorithms;149
6.7;§6. Slightly compressible fluids;158
7;Chapter II The Steady–State Navier–Stokes Equations;168
7.1;Introduction;168
7.2;§1. Existence and uniqueness theorems;168
7.3;§2. Discrete inequalities and compactness theorems;191
7.4;§3. Approximation of the stationary Navier–Stokes equations;210
7.5;§4. Bifurcation theory and non-uniqueness results;234
8;Chapter III The Evolution Navier–Stokes Equations;258
8.1;Introduction;258
8.2;§1. The linear case;258
8.3;§2. Compactness theorems;280
8.4;§3. Existence and uniqueness theorems (n = 4).;289
8.5;§4. Alternate proof of existence by semi-discretization;331
8.6;§5. Discretization of the Navier–Stokes equations: General stability and convergence theorems;342
8.7;§6. Discretization of the Navier–Stokes equations: Application of the general results;375
8.8;§7. Approximation of the Navier–Stokes equations by the Fractional Step Method;406
8.9;§8. Approximation of the Navier–Stokes equations by the artificial compressibility method;437
9;Comments;469
10;References;475
11;Appendix;491
11.1;Implementation of non-conforming linear finite elements;491