Almost classical solutions to the total variation flow

Total Variation Flow and Sign Fast Diffusion in one dimension

“…A concluding remark on the smallness of the time step h. Since we want to describe the behaviour of the TVF, we are mainly interested in the limit h → 0, which means that condition (2. 19) is always fulfilled. Anyway it is interesting to observe that the dynamic becomes more complicated to understand for general values of h, since the "locality" property is lost.…”

“…However, at least in the simpler case of one spatial dimension, the results contained in the present paper exhibit an almost explicit dynamic and a sharp asymptotic behaviour. After the writing of this paper was essentially completed, we learned of a related work [19].…”