 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ib/paper-4/14b/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

v (t, z) = u (t, z + a t)

. Then

v_{t} = κ v_{zz}

and

v (0, z) = u_{0} (z)

. Applying the heat kernel and returning to

x

u (t, x) = \int_{- \infty}^{\infty} K_{t} (x - a t - y) u_{0} (y) d y .

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