An identification problem with evolution on the boundary of parabolic type

We consider an equation of the type A(u + k * u) = f, where A is a linear second-order elliptic operator, k is a scalar function depending on time only and k * u denotes the standard time convolution of functions defined on R with their supports in [0, T]. The previous equation is endowed with dynamical boundary conditions. Assuming that the kernel k is unknown and information is given, under suitable additional conditions k can be recovered and global existence, uniqueness and continuous dependence results can be shown.