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Approximate controllability of linear parabolic equations in perforated domains. (English) Zbl 0964.35015
The authors consider an approximate controllability problem for linear parabolic equations with rapidly oscillating coefficients in a periodically perforated domain. The holes are \(\varepsilon\)-periodic and of size \(\varepsilon\). It is shown that, as \(\varepsilon\) tends to zero, the approximate control and the corresponding solution converge respectively to the approximate control and to the solution of the homogenized problem. Also they prove that the solution of the approximate controllability problem in the perforated domain behaves, as \(\varepsilon\) tends to zero, as that of the problem posed in the perforated domain having as right-hand side the (fixed) control of the limit problem.

MSC:
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35K10 Second-order parabolic equations
93C20 Control/observation systems governed by partial differential equations
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