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Green's function for homogeneous PDE

  1. Feb 16, 2010 #1
    Hi there, could anyone help me on this particularly frustrating problem I am having... I have a linear parabolic homogeneous PDE in two variables with a boundary condition that is a piecewise function.

    I can solve the pde (with a homogeneous BC) however trying to impose the actual BC makes it seem impossible. I think that using Green's functions will help - as I then have a convolution of the green's function with the BC - but I am finding it difficult to find any literature on this case, i.e. homogen pde & nonhomogen BCs.

    Could anyone point me in the right direction? Below is the pde...

    [tex]\frac{\partial u}{\partial t}+ a x \frac{\partial^2 u}{\partial x^2} + b \frac{\partial u}{\partial x}=0[/tex]

    with BC:
    [tex] u(x,T) = x-\rho \,\, \mbox{for}\,\, x>\rho[/tex]
    [tex]\qquad =0 [/tex] otherwise

    Thanks!
     
  2. jcsd
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