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Homework Help: Heat equation

  1. Jul 21, 2010 #1
    u(x,t) defined for x>0 t>0
    d2u/dx2=du/dt

    Conditions:
    u(x,0)=0
    d/dx u(0,t)=-1
    u(x,t) tends to 0 as x tends to infinity
    d2v/dx2 =pv
    d/dx v(0,p) =-1/p

    v(x,p)=integral(0 to inf) exp(-pt) u(x,t) dt

    How do we use this to find v(x,p) and u(0,t)?

    For u(0,t) can we simply integrate wrt x d/dx u(0,t) = -x?


    Thanks in advance
     
  2. jcsd
  3. Jul 21, 2010 #2
    I could be wrong, but isn't there something wrong with the conditions and the way you defined,

    [tex] u(x,t) [/tex]

    ?

    You said,

    [tex] u(x,t)[/tex] [tex] \exists \forall x > 0, t>0 [/tex]

    but in the conditions you are somehow evaluating at,

    [tex] t = 0 [/tex]

    [tex]u(x,0) = 0[/tex]
     
  4. Jul 21, 2010 #3
    You are right. I saw this too but assumed something specific to the heat equation allows it. Or maybe we assume tending to? In any case this is how the question was stated
     
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