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A remark on null exact controllability of the heat equation. (English) Zbl 1002.93025

From the abstract: It is well known that the heat equation \(u_t - \triangle u = f \chi_{\omega}\) in \((0,T) \times \Omega\) with homogeneous Dirichlet boundary conditions is null exactly controllable for any \(T > 0\) and any open nonempty subset \(\omega\) of \(\Omega\). In this note we show that this property may be obtained as a singular limit of the exact controllability properties of singularly perturbed damped wave equations with a changing controller.

MSC:

93C20 Control/observation systems governed by partial differential equations
93B05 Controllability
93C70 Time-scale analysis and singular perturbations in control/observation systems
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