A marine population grows logistically and disperses by diffusion. It is moderately predated on up to a distance $L$ from a straight coast. Beyond that distance, predation is sufficiently excessive to eliminate the population. The density $n(x, t)$ of the population at a distance $x<L$ from the coast satisfies

$$\frac{\partial n}{\partial t}=r n\left(1-\frac{n}{K}\right)-\delta n+D \frac{\partial^{2} n}{\partial x^{2}}$$

subject to the boundary conditions

$$\frac{\partial n}{\partial x}=0 \text { at } x=0, \quad n=0 \text { at } x=L$$

(a) Interpret the terms on the right-hand side of $(*)$, commenting on their dependence on $n$. Interpret the boundary conditions.

(b) Show that a non-zero population is viable if $r>\delta$ and

$$L>\frac{\pi}{2} \sqrt{\frac{D}{r-\delta}}$$

Interpret these conditions.