Comparison of transonic and subsonic solutions of a three-fluid system with cosmic ray diffusion. In this figure, γ_g = 5∕3, γ_c = 4∕3, GM = 1, a = 1, η = 1. Cases with wave damping and/or cooling are compared to the cases without both wave damping and cooling. All cases have the same boundary conditions at the base except D_cb. The diffusive flux (or cosmic ray pressure gradient) at the base is adjusted to get physically allowable solutions (subsonic solutions for the cases without cooling and transonic solution for the cases with cooling). In this example, U_b = 1, P_gb = 2.5, P_cb = 1, , ρ_b = 2∕3, . Dotted line displays the case in which both wave damping and cooling are “OFF” (δ_c = 0, δ⁺ = 0). Left column: dashed, dot-dashed, and solid lines are the cases in which only wave damping is “ON” (δ_c = 0, δ⁺ = 0.1). The three solutions correspond to slightly different D_cb (see text). Middle column: solid line is the case with only cooling is “ON” (δ_c = 0.1, δ⁺ = 0). Right column: solid line is the case in which both cooling and wave damping are “ON” (δ_c = 0.1, δ⁺ = 0.1). Upper row: black, thin brown, and grey lines show the flow speed, the effective sound speed and the Alfvén speed, respectively. Lower row: blue, orange, and green lines show the pressures of the thermal gas, cosmic ray, and forward-propagating wave, respectively.