Time evolution of the total mass of solids (gray line), the mass of dust (black line), and the mass of planetesimals (red line), each normalized to the initial mass of solid in the disk. The black dashed line represents the case where the back reaction is not considered. In this case, the dust pile-up in the inner region of the disk is less significant (due to the fact that dust drift velocities are higher) and the condition for planetesimal formation is not fulfilled. Thus, the dust mass represents the total mass.