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Homogenization and approximate controllability for the heat equation in perforated domains. (Homogénéisation et contrôlabilité approchée de l’équation de la chaleur dans des domaines perforés.) (French. Abridged English version) Zbl 0877.35014
Summary: We study the homogenization and the corrector for the linear heat equation with rapidly oscillating coefficients in a periodically perforated domain. We also consider an approximate controllability problem in this domain, and we study its asymptotic behavior. We obtain as a limit case the approximate controllability of the homogenized problem. In the limit problem, the approximation of the final state is altered by a constant which depends on the proportion of material in the perforated domain and which is equal to 1 when there are no holes.

MSC:
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35K05 Heat equation
35B37 PDE in connection with control problems (MSC2000)
Keywords:
controllability
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