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Constrained PDE : 3D -> 1D

  • Thread starter Ido
  • Start date


I got the following PDE:

I worked with cylindrical coordinates (r,teta,z)
(teta is the angle between the x axis and the r vector (in xy plane))
a,E are constants

I got the constrains: z=0 r=a , so the whole problem is on a simple ring

How can I make the 3D PDE just 1D in teta?
Can I use the Laplasian in cylindrical coordinates, and throw away the d/dr and d/dz?

I hope someone can help me.
Without separation of variables (which I know you don't wanna do), I don't see a way.

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