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Math Help - PDE problem - Separation of variables - Dirichlet condition

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    [Solved] PDE problem - Separation of variables - Dirichlet condition

    Hi all

    I'm in quite some trouble with this PDE problem, that is part of my assignment for wednesday.

    First of all I got the PDE problem:

    PDE: u_t - 2*u_xx = 0 , 0<x<1, t>0

    BC: u(0,t) = t, u(1,t)=0

    IC: u(x,0) = 0


    I then have to show, that v(x,t)=u(x,t)-t(1-x) satisfies

    PDE: v_t - 2*v_xx = -(1-x) , 0<x<1, t>0

    BC: v(0,t) = 0, v(1,t)=0

    IC: u(x,0) = 0


    That is fairly easy.

    Then I have to find a solution for X(x) to the ODE problem:

    ODE: -2*X''(x) = -(1-x)
    BC: X(0) = X(1) = 0

    Again, this is simple, and my result is:

    X(x) = x^2/4 - x^3/12 -x/6

    But then i get in some trouble!
    First I must derive a PDE problem for w(x,t)=v(x,t)-X(x), and then solve it. And after that, I have to find u(x,t)

    To derive the PDE problem, it is just like I did before, and I end up with:

    PDE: w_t - 2*w_xx = 0

    BC: w(0,t) = 0, w(1,t) = 0

    IC: w(x,0) + X(x) = 0



    But how do I solve this? I know, that I should know, but I'm confused, and missed class when this was explaned.
    I'm in desperate need of help.

    Thanks!
    Last edited by SyphonFilter; October 7th 2012 at 02:35 PM. Reason: Found the solution myself :)
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