Question: PDE - Cauchy - Poisson - Fourier

Hello there...

My name's Gilberto and i'm tryin' to make something out of one particular PDE...

Let me span it for you quick:

I'm trying to discover the solution of Cauchy's heat equation for the cirlce S1 = {x mod 2p}, given the following parameters:

ut = uxx, u(0,x) = phi(x), t > 0, x belongs to R

I'm currently thinking that my next step is solving that equation using the Poisson integral. Is that correct?

And after I find the solution of Poisson integral I'm supposed to find the final Fourier solution by using the u(t,x) = a0/2 + sum( (there's more afterwards) .... , t > 0 kinda equation......

I think I've headed in a good direction, but I feel lost in the same time.............

I'm not too good in that mathematics' stuff and I would really love if you were able to give me a little help.

Sincerely yours,

Gilberto