  This paper discusses finite time extinction for a perturbed fast diffusion
equation with dynamic boundary conditions. The fast diffusion equation has the
characteristic property of decay, such as the solution decays to zero in a
finite amount of time depending upon the initial data. In the target problem,
some $p$-th or $q$-th order perturbation term may work to blow up within this
period. The problem arises from the conflict between the diffusion and the blow
up, in the bulk and on the boundary. Firstly, the local existence and
uniqueness of the solution are obtained. Finally, a result of finite time
extinction for some small initial data is presented.
