DOI: 10.68381/jca12016 ISSN: 0944-6532
Homogenization of Changing-Type Evolution Equations
Micol Amar, Andrea Dall'Aglio, Fabio Paronetto
We study the homogenization of the linear equation
R(\varepsilon^{-1}x){\partial u_{\varepsilon}\over\partial t}- \textrm{div} (a(\varepsilon^{-1}x) \cdot \nabla u_{\varepsilon}) = f\,
R
(
ε
−
1
x
)
∂
u
ε
∂
t
−
div
(
a
(
ε
−
1
x
)
⋅
∇
u
ε
)
=
f
with appropriate initial/final conditions, where
R
R
is a measurable bounded periodic function and
a
a
is a bounded uniformly elliptic matrix, whose coefficients
a_{ij}
a
i
j
are measurable periodic functions. Since we admit that
R
R
may vanish and change sign, the usual compactness of the solutions in
L^2
L
2
may not hold if the mean value of
R
R
is zero