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Fourier method | eigenfunctions

  1. Dec 18, 2009 #1
    Use separation of variables/Fourier method to solve
    ut - 4uxx = 0, -pi<x<pi, t>0
    u(-pi,t) = -u(pi,t), ux(-pi,t) = -ux(pi,t), t>0.

    What I got is that (n+1/2)2 are eigenvalues (n=0,1,2,3,...) and cos[(n+1/2)x)] is an eigenfunction.
    Instead of two sets of eigenvalues, there is only one set. I cannot find another set of eigenvalues.
    My question is: is sin[(n+1/2)x)] also an eigenfunction for this problem? Why or why not?

    Thanks for any help!
  2. jcsd
  3. Dec 18, 2009 #2
    Are you sure those are the correct boundary conditions? What problem led you to those boundary conditions? They seem to imply only that u and du/dx are odd functions of x, not that u is smooth at pi.
    Last edited: Dec 18, 2009
  4. Dec 18, 2009 #3
    Yes, I double checked that these are the correct boundary conditions. It is from a PDE course.
  5. Dec 19, 2009 #4
    In that case I don't know. What physical situation do such conditions come from?
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