Unit:
Κατεύθυνση Εφαρμοσμένα ΜαθηματικάLibrary of the School of Science
Author:
Καστάνη Ελευθερία
Supervisors info:
Ι. Στρατής Καθηγητής ΕΚΠΑ (επιβλέπων), Χ. Αθανασιάδης Καθηγητής ΕΚΠΑ, Γ. Μπαρμπάτης Αναπλ. Καθηγητής ΕΚΠΑ
Original Title:
Εισαγωγή στη θεωρία ομογενοποίησης
Translated title:
An introduction to homogenization
Summary:
The aim of this work is to present the mathematical theory of the
homogenization. This theory has been introduced in order to describe the
behaviour of composite materials.Composite materials are characterized by the
fact that they contain two or more finely mixed constituents. They are widely
used nowadays in industry, due to their properties.Generally speaking in a
composite the heterogeneities are small compared to its global dimension. So
two scales characterize the material , the microscopic one , describing the
heterogeneities and the macroscopic one, describing the global behavior of the
composite. From the macroscopic point of view the composite looks like a
“homogeneous” material. The aim of homogenization is precisely to give the
macroscopic properties of the composite by talking into account the properties
of the microscopic structure.To do this there are the following ways. We use
the multiple-scale method, the oscillating test functions method introduced by
L.Tartar and the two scale method which takes into account the two scales of
the problem and introduces the notion of “two scale convergence” .
Keywords:
Homogenization, Tartar, Asymptotic, Multiscale, Equation
