User:Sufian255/sandbox

Theory of Homogenization:
The mathematical theory of homogenization was introduced in 1970’s in order to describe the

'''behavior of composite materials. Homogenization is a mathematical procedure to understand the'''

heterogeneous materials (or media) with highly oscillating heterogeneities (at the microscopic scale)

'''via a homogeneous material. In a composite material, the heterogeneities are small compared to its'''

'''global dimension. So one possible definition would be, it is a process of understanding a heteroge-'''

'''neous (in-homogeneous) media by a homogeneous media. In other words one would like to obtain'''

homogeneous description of a highly oscillating inhomogeneous media via a homogeneous media.

The microscopic scale describes the distribution of heterogeneities and the macroscopic scale de-

'''scribes the global behavior of the composite. The main aim of homogenization theory is to establish'''

'''the macroscopic behavior of a system which is microscopically heterogeneous. Mathematically, it'''

is a theory for studying various problem which includes.

• differential operators with rapidly oscillating coefficients,

• boundary value problems with rapidly changing boundary conditions,

• equations in perforated domains, equations in domain with highly oscillating Boundary.