How to know the variable dependencies of the solution of a PDE?

[torstein]

I'm doing some PDE exercices and I'm having a rough time finding out on which variable my problem depends on. For example, if I have to solve the Laplace equation (or any homogeneous PDE) over a cylinder (or sphere) with Dirichlet (or Neumann or Robin) boundary conditions that depends on z and r, how I know if the solution depends on the angular coordinate?

What I'm doing actually is set the separation of variables and notice that for the angular part I have not any boundary conditions so I can't find a unique solution. Is that a right way to do that?

I know that for the cylinder I have periodical conditions psi(0)=psi(2pi) but it isn't enough right?

Anyway, is there a process that let me find out what variables depends on the solution of an homogeneous PDE?

Thanks.

PS: Sorry for my bad english, isn't my native language.

Edited February 24, 2016 by torstein

[studiot]

Solving such equation generates surfaces over which we sum the flux variable and apply continuity.

 

The flux is obviously sensitive to the area of this surface.

 

So for instance with a cylinder the area depends upon z (the axis) that is how long the cylinder is.

 

It must also depend upon r the radius.

 

But for a complete cylinder the flux is constant we just sum over 0 to 2pi and equate to the source strength.

Edited February 24, 2016 by studiot