Solution
= Solution
The <boundary conditions> are now $C(0,t)=0$ and $C_x(L,t)=0$. Their wave numbers are
$$
k_n=\frac{(n+1/2)\pi}{L},\qquad n=0,1,\ldots.
$$
The principal growth rate is $\mu-D\pi^2/(4L^2)$, so long-term growth occurs when
$$
\mu>\frac{D\pi^2}{4L^2}.
$$
Closing one end reduces the critical growth rate by a factor of four because there is only one absorbing escape boundary.