In this paper we consider an approximate controllability problem for linear parabolic equations with rapidly oscillating coefficients in a periodically perforated domain. The holes are $\epsilon $-periodic and of size $\epsilon $. We show that, as $\epsilon \to 0$, the approximate control and the corresponding solution converge respectively to the approximate control and to the solution of the homogenized problem. In the limit problem, the approximation of the final state is alterated by a constant which depends on the proportion...

In this paper we give a general presentation of the homogenization of Neumann type problems in periodically perforated domains, including the case where the shape of the reference hole varies with the size of the period (in the spirit of the construction of self-similar fractals). We shows that ${H}^{0}$-convergence holds under the extra assumption that there exists a bounded sequence of extension operators for the reference holes. The general class of Jones-domains gives an example where this result applies....

In this paper we consider an approximate controllability problem
for linear parabolic equations with rapidly oscillating coefficients
in a periodically perforated
domain. The holes are -periodic and of size
. We
show that, as ε → 0, the approximate control and
the corresponding solution converge respectively to the
approximate control and to the solution of the homogenized
problem. In the limit problem, the
approximation of the final state is alterated by a constant which
depends
on the
proportion...

In this paper we give a general presentation of
the homogenization of Neumann type problems in periodically perforated
domains, including the case where the shape of the reference hole
varies with the size
of the period (in the spirit of the construction of self-similar fractals).
We shows that
-convergence holds under the extra assumption that
there exists a bounded sequence of extension operators for
the reference holes. The general class
of Jones-domains gives an example where...

The aim of this paper is to provide the correctors associated to the homogenization of a parabolic problem describing the heat
transfer. The results here complete the earlier study in [Jose,
(2009) 189–222]
on the asymptotic behaviour of a problem in a domain with two components separated by an -periodic interface.
The physical model established in [Carslaw and Jaeger, The Clarendon Press, Oxford (1947)] prescribes on the interface the
condition that the flux of the temperature...

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