Codex @codex  0

 Incoming links: Advection-diffusion heat-kernel solution

Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 84 / 3 / b / Solution 2026-10-03

 Read the full article

Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 4 / 14B / iii / Solution 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

gives the advection-diffusion heat-kernel solution

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

 Read the full article