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

The boundary conditions are now $C(0,t)=0$ and $C_x(L,t)=0$. Their wave numbers areThe principal growth rate is $\mu -D{\pi }^2/(4L^2)$, so long-term growth occurs whenClosing one end reduces the critical growth rate by a factor of four because there is only one absorbing escape boundary.