  The decay of a crystalline cone below the roughening transition is studied.
We consider local mass transport through surface diffusion, focusing on the two
cases of diffusion limited and attachment-detachment limited step kinetics. In
both cases, we describe the decay kinetics in terms of step flow models.
Numerical simulations of the models indicate that in the attachment-detachment
limited case the system undergoes a step bunching instability if the repulsive
interactions between steps are weak. Such an instability does not occur in the
diffusion limited case. In stable cases the height profile, h(r,t), is flat at
radii r<R(t)\sim t^{1/4}. Outside this flat region the height profile obeys the
scaling scenario \partial h/\partial r = {\cal F}(r t^{-1/4}). A scaling ansatz
for the time-dependent profile of the cone yields analytical values for the
scaling exponents and a differential equation for the scaling function. In the
long time limit this equation provides an exact description of the discrete
step dynamics. It admits a family of solutions and the mechanism responsible
for the selection of a unique scaling function is discussed in detail. Finally
we generalize the model and consider permeable steps by allowing direct adatom
hops between neighboring terraces. We argue that step permeability does not
change the scaling behavior of the system, and its only effect is a
renormalization of some of the parameters.
