Change in the branch period of the step pattern formed by a moving linear source-initial coarsening and effect of an abrupt change in the velocity

► We study pattern formation of a step induced by a moving linear source of adatoms. ► It explains a comb-like step pattern observed during Ga deposition on Si(111), and possibly in a graphene film grown on SiC. ► Coarsening process of the branch period is examined and power laws are found. ► Change in the step pattern with an abrupt change in the source velocity is also studied.