We study pattern formation of a step induced by a moving linear source of adatoms, which is related to a step pattern during Ga deposition on Si(111), and possibly to a graphene film grown on SiC. Diffusion of adatoms released from the source in front of the step causes wandering instability of the step. Many small intrusions with branches appear, and the characteristic length of the pattern increases until it reaches a steady state. Coarsening process of the branch period is examined. In the first stage the period increases as lambda similar to t(v1), with v(1) approximate to 1/4, increasing slowly with decreasing the velocity of the source. Competition between the intrusions results in a faster growth of the branch period with exponent v(2) approximate to 1/2. Change in the step pattern by an abrupt change in the source velocity is also studied. Branches adjust their period by terminating growth of some branches or increasing their number by tip-splitting. The latter is suppressed by a large stiffness and a metastable state with side branches is seen. (c) 2012 Elsevier B.V. All rights reserved.