Stability result for a time dependent potential in a waveguide

We consider the operator $H:={\mathrm{\partial }}_t-\mathrm{\Delta }+V$ in 2D or 3D waveguide. With an adapted global Carleman estimate with singular weight functions we give a stability result for the time dependent part of the potential for this particular geometry. Two cases are considered: the bounded waveguide with mixed Dirichlet and Neumann conditions and the open waveguide with Dirichlet boundary conditions.