The 2D diffusion equation is to be solved within the problem domain: a
disk of radius a. There are N constant point sources of mass within the
disk, and Dirichlet b.c. at the edge r = a, given by the function
f(theta) = U(a,theta).

Am I correct in thinking that the steady state solution for U(r,theta)
can be computed as the sum of the N Green's functions corresponding to
the sources (with the b.c. U(a,theta) = 0) and the Poisson's integral
formula corresponding to the boundary function f?

Thanks.
yes:

In article <g0e5md$bko$1 at (no spam) lust.ihug.co.nz>,
Gib Bogle <bogle at (no spam) ihug.too.much.spam.co.nz> writes:
The 2D diffusion equation is to be solved within the problem domain: a
disk of radius a. There are N constant point sources of mass within the
disk, and Dirichlet b.c. at the edge r = a, given by the function
f(theta) = U(a,theta).

Am I correct in thinking that the steady state solution for U(r,theta)
can be computed as the sum of the N Green's functions corresponding to
the sources (with the b.c. U(a,theta) = 0) and the Poisson's integral
formula corresponding to the boundary function f?

Thanks.
yes:

Delta u(i) = f(i) on D , u=0 on \partial D i=1,..,N
f(i) representing the source terms
Delta u(N+1) = 0 on D , u=f on \partial D

let
v= sum_{i=1,...,N+1} u(i)
=
Delta v = sum_{i=1,..,N} f(i) on D, v=f on \partial D


hth
peter