  We study a singular one-dimensional parabolic problem with initial data in
the $BV$ space, the energy space, for various boundary data. We pay special
attention to Dirichlet conditions, which need not satisfied in a pointwise
manner. We study the facet creation process and the extinction of solutions
caused by the evolution of facets. Our major tool is the comparison principle
provided by the theory of viscosity solutions developed in \cite{miyory}.
