多尺度问题——理论、数值逼近及应用 (国内英文版)

     The focus of this is on the lgest developments related to the analysis of problems in which several scales are presented.After a theoretical presentation of the theory of homogenization in the periodic case, the other contributions address a wide range of applications in the fields of elasticity (asymptotic behavior of nonlinear elastic thin structures, modeling of junction of a periodic family of rods with a plate) and fluid mechanics (stationary Navier-Stokes equations in porous media). Other applications concern the modeling of new composites (electromagnetic and piezoelectric materials)and imperfect transmission problems. A detailed approach of numerical finite element methods is also investigated.

Preface
Alain Damlamian
An Introduction to Periodic Homogenization
Alain Damlamian
The Periodic Unfolding Method in Homogenization
Gabriel Nguetseng and Lazarus Signing
Deterministic Homogenization of Stationary Navier-Stokes
Type Equations
Patricia Donato
Homogenization of a Class of Imperfect Transmission Problems
Georges Griso
Decompositions of Displacements of Thin Structures
Georges Griso
Decomposition of Rods Deformations. Asymptotic Behavior of
Nonlinear Elastic Rods
Dominique Blanchard
Junction of a Periodic Family of Rods with a Plate
in Elasticity
Bernadette Miara
Multi-scale Modelling of New Composites: Theory and
Numerical Simulation
Assyr Abdulle
A Priori and a Posteriori Error Analysis for Numerical
Homogenization: A Unified Framework