Null controllability of the heat equation as singular limit of the exact controllability of dissipative wave equation under the Bardos-Lebeau-Rauch geometric control condition. (Q1416339)

The author approaches null controllability of the heat equation \[ {\partial y(t, x) \over \partial t} = \Delta y(t, x) + u(t, x) \chi_\omega(x) \quad (x \in \Omega), \qquad y(t, x) = 0 \quad (x \in \Gamma) \] in a domain \(\Omega\) with boundary \(\Gamma\) \((\chi_\omega(x)\) the characteristic function of a subdomain) looking at the equation as limit of the singularly perturbed wave equation \[ \varepsilon {\partial^2 y(t, x) \over \partial t^2} + {\partial y(t, x) \over \partial t} = \Delta y(t, x) + u(t, x) \chi_\omega(x) \quad (x \in \Omega), \qquad y(t, x) = 0 \quad (x \in \Gamma). \] The theorems extend and/or simplify existing results included in the references.