 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2005/ii/paper-2/13e/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

t = β_{u} τ, s = x β_{u} / D_{u}, Q = \frac{β _{v}}{β _{u}}, P = \frac{D _{v} β _{u}}{D _{u} β _{v}} .

The chain rule gives

\partial_{τ} = β_{u} \partial_{t}

and

\partial_{x}^{2} = (β_{u} / D_{u}) \partial_{s}^{2}

. Dividing the first equation by

β_{u}

and the second by

β_{v}

gives the required scaled reaction–diffusion system. Positive degradation and diffusion constants are assumed.

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