A new Carleman inequality for a heat equation in presence of singularities and controllability consequences (Q2660553)

The following control problem \[y_{t}-\Delta y+ ay=v\mathbf{1}_{\omega}\] is considered, where \(\mathbf{1}_{\omega}\) is the characteristic function of the set \(\omega\), a nonempty subset of \(\Omega\) and \(v\) is a control function. Compared with existing results, in this paper, the domain \(\Omega\) has one reentrant corner of angle. This allows the solution to exhibit singularities near the corner as well as at the points where the mixed boundary conditions meet. A Carleman inequality is established by constructing a convenient weight function. The null controllablility is also proved.