Yes you can, and it turns out that there are only nonzero solutions in case a = 0 or a = 1/(2*ln(2)), and in those cases there are infinitely many solutions.
However, it doesn't strike me as obvious that just because the BC's are radially symmetric, it must follow that the entire solution is...
No. The question is not whether there are radially symmetric solutions for other values of a, but whether there are any solutions. The solution could be theta-dependent (unless the fact that the BC's are radially symmetric implies that the solution is, but I don't think this is true).
In...
OK, the full question is this:
I'm given the 2D Laplace equation in circular polars. The problem is defined on the annulus
1<= r <= 2.
The boundary conditions are
a*u + diff(u,r) = 0
on r=1 and r=2.
The question says: show there are nonzero solutions if a = 0 or a =...
Homework Statement
I'm considering Laplace's equation in 2D, written in circular polar coordinates (so that's u_rr + 1/r*u_r + (1/r^2)*u_theta,theta). I've worked out what all the seperable solutions are.
My question is: is this set of seperable solutions complete.
(That is, can all...