  A continuum model for the dynamics of a single step with the strongly
anisotropic line energy is formulated and analyzed. The step grows by
attachment of adatoms from the lower terrace, onto which atoms adsorb from a
vapor phase or from a molecular beam, and the desorption is non-negligible (the
"one-sided" model). Via a multi-scale expansion, we derived a longwave,
strongly nonlinear, and strongly anisotropic evolution PDE for the step
profile. Written in terms of the step slope, the PDE can be represented in the
form similar to a convective Cahn-Hilliard equation. We performed the linear
stability analysis and computed the nonlinear dynamics. Linear stability
depends on whether the stiffness is minimum or maximum in the direction of the
step growth. It also depends nontrivially on the combination of the anisotropy
strength parameter and the atomic flux from the terrace to the step.
Computations show formation and coarsening of a hill-and-valley structure
superimposed onto a large-wavelength profile, which independently coarsens.
Coarsening laws for the hill-and-valley structure are computed for two
principal orientations of a maximum step stiffness, the increasing anisotropy
strength, and the varying atomic flux.
