Radial profile of the surface densities of the gas and the dust particles at different time snaps t = 10⁵,3 × 10⁵ and 10⁶   yr with a₀ = 1   mm and ϱ_p = 1.0   g   cm^-3. The parameter are α = 10^-3 and Σ_d/Σ_g = 10^-2 at t/t_K = 0. The solid lines correspond to the dust surface density while the gas surface density is shown using the dashed lines. The dotted line refers to Σ_g ~ R^-1 at t/t_ν = 0. The profiles shown in the left panel are obtained using the boundary conditions of Takeuchi & Lin (2005). Moving the inner boundary to smaller R and applying an analytical prescription for Σ_g at the inner and outer boundary cause the profiles to change as shown in the right panel.