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Is there a way to transform the PDE:
enter image description here

Into a Sturm-Liouville problem with a clearly identified weight function, thanks to the method of separation of variables? I am stuck on this problem.

Many thanks in advance.

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  • $\begingroup$ Were you able to separate variables? What is the region? Is it $0 \le r < \infty$ and $0 \le \theta\le 2\pi$, or some subset of that? $\endgroup$ Jan 5, 2023 at 19:03
  • $\begingroup$ It was the case of a sector ring I was facing. But does it matter to find the Sturm Liouville problem? I just managed to find the SL form and it is (rR')' +(1/r)k²R = 0 , so with weight function 1/r ! Thank you for trying to help $\endgroup$
    – c.leblanc
    Jan 6, 2023 at 0:21
  • $\begingroup$ I'm glad you found what you wanted. To me, a well-posed Sturm-Liouville equation also requires endpoint conditions such as periodicity, boundedness, or homogeneous endpoint conditions, for example. That's why I was asking for more details. $\endgroup$ Jan 7, 2023 at 1:09
  • $\begingroup$ I thought you meant it could change de weight function. But with the meaning you just explained, you are totally right. Indeed my problem had such homogeneous conditions. $\endgroup$
    – c.leblanc
    Jan 7, 2023 at 13:28

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