Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 3 / 13A / a / iii / Solution

At late times the first sine mode dominates, with growth exponentThusand the population grows precisely when $\mu >{\mu }_c$. Faster diffusion carries organisms to the lethal ends more quickly and raises the threshold; a longer channel lowers the principal diffusion eigenvalue and therefore lowers the threshold.