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Approximate controllability for linear parabolic equations with rapidly oscillating coefficients. (English) Zbl 0815.93041
Summary: We consider linear parabolic equations with rapidly oscillating coefficients in a bounded domain $$\Omega$$ of $$\mathbb{R}^ n$$ with Dirichlet type homogeneous boundary conditions. Under some natural assumptions on the coefficients we prove that, for any fixed positive time, the system may be approximately controlled in a uniform way with respect to the oscillation parameter with controls supported in any open subset of $$\Omega$$. More precisely, we prove that the controls remain bounded when the oscillation parameter tends to zero and that they converge strongly in $$L^ 2$$ to a control for the homogenized parabolic system.

##### MSC:
 93C20 Control/observation systems governed by partial differential equations 93B05 Controllability 93C05 Linear systems in control theory