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Heat equation problem is killing me.

  1. Apr 23, 2012 #1
    1. The problem statement, all variables and given/known data

    vt(x,t)=vxx(x,t) + p(x,t),
    Neumann boundary conditions,
    v(x,0)=cos(∏x)

    2. Relevant equations

    Assume v(x,t)=X(x)T(t)

    3. The attempt at a solution

    I'm stuck. We aren't given a p(x,t) and I'm not sure what to do. Where do I go from here?

    Attempt so far:

    screen-capture-10-3.png
     
  2. jcsd
  3. Apr 24, 2012 #2
    So I got a little farther .......

    The full solution is

    e-n22tcos(∏x) + Ʃe-n22t(∫[0,t]pn(t)en22tdt)cos(n∏x).

    But I still can't figure out any more information without knowing what exactly p(x,t) is. (Right?) I'm asked to solve the equation and then explain "For what forcing does the temperature eventually settle down to a constant." Thoughts?


    EDIT: Also, I know that pn(t)=∫[0,1]p(y,t)cos(n∏y)dy, though I can't figure this out (Can I?) unless I'm explicitly told what p(y,t) is.
     
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