  We describe a PDE model of bedrock abrasion by impact of moving particles and
show that by assuming unidirectional impacts the modification of a geometrical
PDE due to Bloore exhibits circular arcs as solitary profiles. We demonstrate
the existence and stability of these stationary, travelling shapes by numerical
experiments based on finite difference approximations. Our simulations show
that, depending on initial profile shape and other parameters, these circular
profiles may evolve via long transients which, in a geological setting, may
appear as non-circular stationary profiles.
