= 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 approaches
$$
C(x,t)\sim \frac{4C_0}{\pi}\sin\frac{\pi x}{L}
e^{(\mu-\mu_c)t}.
$$
For $\mu<\mu_c$ 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.
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