Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?