Homogenization of Non-Linear Variational Problems with Thin Low-Conducting Layers |
| |
Authors: | Andrea Braides Marc Briane |
| |
Institution: | (1) Dipartimento di Matematica, Universita di Roma "Tor Vergata", Via della Ricerca Scientifica, 00133, Roma, Italy;(2) Centre de Mathematiques, I.N.S.A. de Rennes & I.R.M.A.R., 20 avenue des Buttes de Coesmes, 35043, Rennes Cedex, France |
| |
Abstract: | This paper deals with the homogenization of a sequence of non-linear conductivity energies in a bounded open set
The energy density is of the same order as
where
is periodic, u is a vector-valued function in
and
The conductivity
is equal to 1 in the "hard" phases composed by
two by two disjoint-closure periodic sets while
tends uniformly to 0 in the "soft" phases composed by periodic thin layers which separate the hard phases. We prove that
the limit energy, according to γ-convergence, is a multi-phase functional equal to the sum of the homogenized energies (of
order 1) induced by the hard phases plus an interaction energy (of order 0) due to the soft phases. The number of limit phases
is less than or equal to N and is obtained by evaluating the γ-limit of the rescaled energy of density
in the torus. Therefore, the homogenization result is achieved by a double γ-convergence procedure since the cell problem
depends on ε. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|