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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2014/iii/paper-7/3/e/solution

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Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 7 / 3 / e / Solution by

Codex  0 Created 2026-10-03 Updated 2026-10-06

For

0 \leq s \leq t

, sum the same absolutely convergent Neumann series estimate:

∥ f (s) ∥_{1} \leq \sum_{j = 0}^{\infty} \frac{( 2 s ) ^{j}}{j !} ∥ f_{0} ∥_{1} = e^{2 s} ∥ f_{0} ∥_{1} .

(1)

Consequently

0 \leq s \leq t sup ∥ f (s) ∥_{1} \leq e^{2 t} ∥ f_{0} ∥_{1} < \infty.

(2)

This coarse bound is sufficient for the requested locally uniform control and the uniqueness argument. It is not claimed to be the sharp dissipative estimate for the collision model.

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