19.3.3.1 Solution pnfd-a

Question:

Perform the equivalent analysis in the three dimensional case.

Answer:

One difference is that the Green’s function is different.

Another difference is in the behavior of the solution at large distances. In three dimensions:

$$u_{\rm {out}} \sim C_1 + \frac{C_2}{\rho} + \ldots$$

However, the final answer turns out to be very similar. (Of course, area integrals become volume integrals and contour integrals become surface integrals.)