DOI: 10.68381/jca11022 ISSN: 0944-6532
Homogenization of Evolution Problems in a Fiber Reinforced Structure
Michel Bellieud
We study the homogenization of parabolic or hyperbolic equations like
\rho_\epsilon(x){\partial^n u_\epsilon \over \partial t^n}- div(a_\epsilon(x) \nabla u_\epsilon) =f
ρ
ϵ
(
x
)
∂
n
u
ϵ
∂
t
n
−
d
i
v
(
a
ϵ
(
x
)
∇
u
ϵ
)
=
f
on
\Omega\times (0, T)
Ω
×
(
0
,
T
)
plus boundary conditions,
n \in \{1,2\}
n
∈
{
1
,
2
}
, where the coefficients
a_\epsilon
a
ϵ
and
\rho_\epsilon
ρ
ϵ
takes values of very different order on an
\epsilon
ϵ
-periodic subset
T_\epsilon \subset \Omega
T
ϵ
⊂
Ω
(fibered structure) and elsewhere. We find a non local effective equation deduced from a homogenized system of several equations.