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Diffusion equation with Dirichlet BC

  1. Oct 6, 2012 #1
    1. The problem statement, all variables and given/known data
    Solve ut=kuxx
    u(x,0)=0 (ψ(x))
    u(0,t)=1
    on the half line 0<x<infinity
    (exercise 2, 3.1, Strauss)


    2. Relevant equations



    3. The attempt at a solution
    There are two bits I don't get:

    First, I know I have to make an odd or even extension to the whole line. But for both even and odd extensions, the formulae are:
    u(x,t)=1/(√4∏kt)(∫(e-(x-y)2/4kt±e-(x+y)2/4kt)ψ(y)dy)
    this means for u(x,0)=0, everything is multiplied by 0, which clearly isn't right.

    Second, I don't know which extension to apply, it seems like both should work: I can either make an odd extension about the line x=1 or an even extension about the t axis, both will intercept the t axis at 1, hence satisfying the BC.

    Any help would be greatly appreciated!
     
  2. jcsd
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