the isobaric approximation and a more simplified cooling rate. @IIK06 also found them as the finite extent solutions, and they truncated the solution at the first peak of the temperature profile near the transition front. We call this type of solutions ‘C-U-o’ solutions, where ‘C-U’ means solutions connecting CNM and unstable phase, and ‘o’ means the oscillation.

[*C-U Solutions.*]{} For larger mass flux $j=25j_\mathrm{ZP}$, the topological properties of the stationary point of the unstable phase changes from spiral to node (see the first row of figure \[fig:j0\]c) . Thus, from the second row of figure \[fig:j0\](c), there is no oscillation in the temperature profile, and the CNM is monotonically connected with the unstable phase. Figure \[fig:large\_flux\] shows solutions for much larger mass flux, $j/j_\mathrm{ZP}=25$, 1000, 2000, and 3000. One can see that as the mass flux increases, the density (pressure) of the unstable phase at $x=\infty$ increases (decreases) along the equilibrium curve. Because of large mass flux, the pressure increases significantly toward the CNM. This type solutions with lower mass flux already has been found in @Eetal92 under isobaric approximation. We call this type of solutions ‘C-U’ solutions.

![ Trajectories of solutions for $j/j_\mathrm{ZP}=1$(the solid line), 1000(the dashed line), 2000(the 