Find steady-state solution Governing equation: 
$$\frac{\partial \Omega}{\partial t} = \frac{\partial^2 \Omega}{\partial x^2} -DH \frac{\partial \Omega}{\partial x} $$
Find the steady-state solution $\Omega(x)$ from the governing equation with boundary conditions $\Omega(0) = 1$ and $\Omega(1) = 0$.

The steady state solution occurs when $\Omega_t = 0$.  The steady-state obeys the equation (assuming $DH$ is a constant)
$$\Omega''(x) - DH \Omega'(x) = 0$$
with BC's $\Omega(0) =1$ and $\Omega(1)=0$.  The solution is
$$\Omega(x) = A+B e^{DH x}$$
where $A+B = 1$ and $A + B e^{DH} = 0$.
