section \[sec:numerical\]. In section \[sec:ZP\], we briefly review the solutions connecting the CNM and WNM derived by ZP69. In section \[sec:dynamical\], we present solutions describing dynamical transition layer that has larger mass flux than ZP69. The results are discussed in section \[sec:discuss\] and are summarized in section \[sec:summary\].

Basic Equations and Numerical Methods {#sec:numerical}
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Basic equations for radiative gas under the plane-parallel geometry are the continuity equation, $$\frac{\partial \rho}{\partial t} + \frac{\partial}{\partial x}(\rho v)=0,
        \label{eoc}$$ the momentum conservation, $$\frac{\partial \rho v}{\partial t} + \frac{\partial}{\partial x}\left( P + \rho v^2 \right)=0,
        \label{eom}$$ the energy equation, $$\frac{\partial E}{\partial t} +
        \frac{\partial}{\partial x}\left[ \left( E+P \right)v - \kappa \frac{\partial T}{\partial x} \right]
        = - \rho{\cal L}(\rho,T),
        \label{eoe}$$ and the equation of state, $$P={\cal R} \rho T
        \label{eos}$$ where $E=\rho v^2/2 + P/(\gamma-1)$ is the total energy, and $\gamma=5/3$ is the ratio of specific heats, $\kappa$ is the coefficient of heat conductivity, and ${\cal L}(\rho,T)$ is the net cooling rate per unit mass, ${\cal R}=k_\mathrm{B}/m_\mathrm{H}$ is the gas constant, and $m_\mathrm{H}$ is the hydrogen mass. Throughout in this paper we assume a gas consists of atomic hydrogen. For the range of temperatures considered, since the gas is almost neutral, we adopt $\kappa=2.5\times10^3\sqrt{T}$ cm$^{-1}$ 