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Homework Help: Two dimensional heat equation with source

  1. Mar 31, 2010 #1
    I have the following PDE

    PDE: ut=A2(uxx+uyy)+f(x,y,t) such that A is a constant
    BC: ux(1,y,t)=0
    ux(0,y,t)=0
    uy(x,1,t)=0
    u(x,0,t)=0
    IC: u(x,y,0)=0

    I've set up my ODEs using seperation of variables to get

    X''/X=k1 Y''/Y=k2 T'/(A2)T=k1+k2

    where k1 and k2 are constants.



    How do I account for my source term (f(x,y,t))? I'm reading up on eigenfunction expansion but so far it's only for the dimensional case.
     
    Last edited: Mar 31, 2010
  2. jcsd
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