- #1
wumple
- 60
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Hi,
When can I assume that the solution the laplace equation (or poisson equation) is radial? That is, when can I look only at (in polar coordinates)
[tex]\frac{\partial u^2} {\partial^2 r} + \frac{1}{r} \frac{\partial u} {\partial r} = f(r,\theta)[/tex]
instead of
[tex]\frac{\partial u^2} {\partial^2 r} + \frac{1}{r} \frac{\partial u} {\partial r} + \frac{1}{r^2}\frac{\partial u^2} {\partial^2 \theta} = f(r,\theta)[/tex]
With appropriate boundary conditions of course. My guess is any time that the boundary conditions are constant in theta and f depends only on r? But I'm not really sure.
Thanks for any help!
-wumple
When can I assume that the solution the laplace equation (or poisson equation) is radial? That is, when can I look only at (in polar coordinates)
[tex]\frac{\partial u^2} {\partial^2 r} + \frac{1}{r} \frac{\partial u} {\partial r} = f(r,\theta)[/tex]
instead of
[tex]\frac{\partial u^2} {\partial^2 r} + \frac{1}{r} \frac{\partial u} {\partial r} + \frac{1}{r^2}\frac{\partial u^2} {\partial^2 \theta} = f(r,\theta)[/tex]
With appropriate boundary conditions of course. My guess is any time that the boundary conditions are constant in theta and f depends only on r? But I'm not really sure.
Thanks for any help!
-wumple
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