Past exam of the mathematics course of the University of Cambridge 2023 iii Paper 105 3 b Solution 2026-09-28
The Strong Huygens principle in three spatial dimensions says that the solution at depends only on the initial data on the sphererather than on the full ball bounded by that sphere. This follows immediately from the Kirchhoff formula and its time derivative. Consequently a disturbance has no tail inside the light cone: if the initial data are supported in a compact set , then whenever that sphere misses . This is sharper than finite propagation speed, which only excludes influence from outside the ball.