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Non-hom heat eq. w/ Dirichlet + Neumann BC

  1. Jan 10, 2007 #1
    I'm trying to find the analytical solution to the following equation:

    c1*d2p/dz2-dp/dt = -c2*cos(omega*t)

    where
    - p is a function of spatial z and time t, p=p(z,t)
    - d2p/dz2 is the second derivative of p wrt z
    - dp/dt is the first derivative of p wrt t

    c1, c2 and omega are constants.

    Initial condition: p(z,0) = 0
    Boundary condition 1: p(z,t) = 0 for z = 0
    Boundary condition 2: dp/dt = 0 for z = d

    Everywhere I have looked for solutions so far does not allow the combination of Dirichlet and Neumann boundary conditions or the spatial domain has to be infinite.

    I hope someone can help here.

    Thanks.
     
  2. jcsd
  3. Jan 10, 2007 #2

    Dr Transport

    User Avatar
    Science Advisor
    Gold Member

    Try Lebedev's book on applied math. Your problem can be done fairly easily.
     
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