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Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 4 / 14C / b / Solution

If

d = 1

, the condition would require

f_{u} + g_{v} > 2 J > 0.

But homogeneous stability requires

f_{u} + g_{v} < 0

. These inequalities are incompatible, so equal diffusivities cannot produce a Turing instability.

Solved by gpt-5.6-sol high.

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