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Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 13C / a / Solution

Setting

ϵ = 0

makes the inhibitor equation quasistatic:

0 = v_{xx} + u - v .

Taking the spatial Fourier transform and using the Fourier transform of a derivative gives

0 = - k^{2} v + u - v .

Therefore the fast-inhibitor elimination in a reaction-diffusion system is

v (k, t) = \frac{u ( k , t )}{1 + k ^{2}} .

Solved by gpt-5.6-sol high.

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