advances in the fabrication of small devices have stimulated interest in low-temperature kinetic processes on crystal surfaces. in most experimental situations, nanoscale solid structures decay with time having a lifetime that typically is a large power of the feature size and increases with decreasing temperature. strategies for skirting the lifetime limitations involve processing at ever-lower temperatures for ever-smaller structure sizes. at temperatures below the roughening transition crystal surfaces evolve via the motion of interacting steps at the nanoscale, and may develop macroscopically flat parts known as ``facets''. the mathematical description of surface evolution at such temperatures is an area of intensive research. \vskip .1in \noindent the subject of this talk is a continuum description of the morphological relaxation of crystal surfaces in $(2+1)$ dimensions below the roughening temperature by use of $pdes$. for processes limited by the diffusion of point defects (``adatoms'') on terraces between steps and the attachment and detachment of atoms to and from steps, the surface height profile outside facets is described via a nonlinear, fourth-order $pde$ that accounts for step line-tension energy $g1$ and step-step repulsive interaction energy $g3$. the $pde$ is derived from the difference-differential equations for the motion of individual steps, and, alternatively, via a continuum surface free energy. particular solutions to the $pde$ are shown to plausibly unify experimental observations of decaying biperiodic surface profiles. to further test the $pde$, the facet evolution of axisymmetric profiles is treated analytically as a free-boundary problem. for long times, axisymmetric shapes and $g3/g1< 1$, singular perturbation theory is applied for self-similar shapes close to the facet. scaling laws with $g3/g1$ are derived for the boundary-layer width, maximum slope and facet radius; and a universal $ode$ for the slope profile is derived and solved uniquely via applying effective boundary conditions at the facet edge. the scaling results compare favorably with numerical solutions of the difference-differential equations for the step positions.