Quote by coomast
Hope this helps you one step further.

Hello coomast
Thank you very much for your answer. You make special comments that make me further understand small details I haven't understand yet.
After doing some research, as much as I understand now, the problem is indeed complicated and not trivial. During all this thread I have tried to split the problem and state basic questions because my knowledge and experience in PDE is very limited.
To reduce the complexity splitting the problem was based on:
1. 2D steady heat conduction, no transients, no time dependency, no phi dependency, dependencies only on r and z
2. For a first try the heat source considered as uniform
3. For a first try not von Neumann boundary conditions, the heat needs to enter the cylinder from the upper part, all other sides are insulated
The equation is following:
[tex]\frac{g(r,z)}{k} =
\frac{\partial^2 u}{\partial r^2}+\frac{1}{r} \cdot
\frac{\partial u}{\partial r}+\frac{\partial^2 u}{\partial z^2} [/tex]
From this link
http://www.engr.unl.edu/~glibrary/gl...05b/node4.html what I understand is that the function g(r,z) is the heat source. They give a solution with green functions, unfortunately I don't understand them to implement a program.
If the heat souce is constant the equation is following:
[tex]\frac{u_0}{k} =
\frac{\partial^2 u}{\partial r^2}+\frac{1}{r} \cdot
\frac{\partial u}{\partial r}+\frac{\partial^2 u}{\partial z^2} [/tex]
Unfortunately I began to loose focus and my post can't be well formulated, my apologies
Best Regards
phioder
PS: What does it mean that a solution is "bounded" or "not bounded"