Stability result for a time dependent potential in a waveguide

We consider the operator $H:= \partial_t -\Delta+V$ in $2$D or $3$D 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.