Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 154 / 2 / 5

Table of contents
- Solution 5

Solution

For a radial function in three dimensions,

Δ u = u_{rr} + \frac{2}{r} u_{r} = \frac{1}{r} \partial_{rr} (r u) .

w = r u

. Multiplying the wave equation by

r

gives the radial reduction of the three-dimensional wave equation

w_{tt} - w_{rr} + \frac{∣ w ∣ ^{p - 1} w}{r ^{p - 1}} = 0, r > 0,

with the regularity boundary condition

w (t, 0) = 0

.

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version