and cooling length in the solution. Thus, the critical mass flux is a function of $P_\mathrm{c}$. The actual value of $j_\mathrm{crit}$ is shown by the solid line in figure \[fig:sol\_diag\]. In most range of $P_\mathrm{c}$, $j_\mathrm{crit}$ lies in the region occupied by the C-U solutions.

For $|j|>|j_\mathrm{crit}|$, advection dominates heat conduction in energy transfer. In this case, the thickness of the front is characterized by the cooling length instead of the Field length. In typical ISM, $l_\mathrm{F}/l_\mathrm{c}$ is roughly as small as $10^{-2}$. Therefore, as the mass flux increases, the thickness of the front increases. Figure \[fig:jcrit\_profile\] shows the temperature profiles for $j=j_\mathrm{ZP}$, $j_\mathrm{crit}$, $5j_\mathrm{crit}$, and $10j_\mathrm{crit}$. The CNM pressure is set to $P_\mathrm{c}/k_\mathrm{B}=3000$ K cm$^{-3}$. One can see that the thickness of the layer increases with the mass flux.

![ Temperature profiles for $j=j_\mathrm{ZP}$(the solid line), $j_\mathrm{crit}$(the dashed line), $5j_\mathrm{crit}$(the dotted line), and $10j_\mathrm{crit}$(the dot-dashed line). The CNM pressure is set to $P_\mathrm{c}/k_\mathrm{B}=300$ K cm$^{-3}$. []{data-label="fig:jcrit_profile"}](fig6.eps){width="8.0cm"}

Transition Layers for $P_\mathrm{c}>P_\mathrm{max}$ {#sec:gt Pmax}
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In previous section, we found solutions only for $P_\mathrm{min}<P_\mathrm{c}<P_\mathrm{max}$. However, in actual ISM, the CNM pressure can be greater than $P_\mathrm{max}$, for example, in shock-compressed regions. Our solutions can be directly extend for $P_\mathrm{c}>P_\mathrm{max}$.

Figure \[fig:sol\_diag\] 