# LaPlace Equation in Polar

1. Feb 15, 2010

### EsponV

1. The problem statement, all variables and given/known data
Solve the Laplace equation: delta u = d2u/dx2+d2u/dy2
inside the half disk 0<r<R, 0<phi<pi
Temperature on the bottom side of the disk is zero, u(x,y=0)=0. Temperature on the upper side of the disk is u(r=R, theta) = u0(phi), 0<phi<pi

2. Relevant equations
I'm assuming the Laplace equation and the given bc conditions

3. The attempt at a solution
I attempted the solution, which I think up until this point is correct, but I've gotten stuck trying to figure out the constants.

http://img708.imageshack.us/img708/707/p2150074.jpg [Broken]

Thank you all for your help.

Last edited by a moderator: May 4, 2017
2. Feb 16, 2010

### EsponV

I just got a email telling me I had a response, however I don't see it in the thread. Anyhow, the picture that only shows half the page of paper because that's all the work I had done on it. I got stuck at that point and wasn't sure how to go about calculating the unknown constants (if I had done everything correctly to that point).