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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.

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