 Solution

Immediately after $t=0$, thin boundary layers enforce zero concentration at both ends while the interior remains close to $C_0$. The profile is symmetric about $L/2$. Higher sine modes then decay rapidly and the shape approachesFor $\mu <{\mu }_c$ successive late-time curves have the same sine shape and decreasing height; for $\mu >{\mu }_c$ they have that shape and increasing height. Those features determine the two requested sketches.