  We present a new formulation and generalization of the classical theory of
heat conduction with or without fading memory which includes the usual heat
equation subject to a dynamic boundary condition as a special case. We
investigate the well-posedness of systems which consist of Coleman-Gurtin type
equations subject to dynamic boundary conditions, also with memory. Nonlinear
terms are defined on the interior of the domain and on the boundary and subject
to either classical dissipation assumptions, or to a nonlinear balance
condition in the sense of [11]. Additionally, we do not assume that the
interior and the boundary share the same memory kernel.
