Homogenization of a highly rarefied binary structure of finite diffusivity

Abstract

The homogenization of a binary structure made of very small particles of general shape is performed when the diffusivity is finite and when the size of the particles has a critical value with respect to a rarefaction number. The limit problem involves an auxiliary function which can be interpreted as the solution of a problem of cellular type, thus filling the gap with classical methods of multiple scales.

Keywords:

• Homogenization
• Multiple scale method
• Diffusion
• Binary structure

Keywords:

• 2000 Mathematics Subject Classifications
• 35B27
• 35Q72
• 74Q05
• 74Q15
• 76M50