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Math Help - defining Heat Equation

  1. #1
    Junior Member
    Joined
    Dec 2009
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    31

    Red face defining Heat Equation

    Define v(x,t) = u(x,t) - Ue (x)
    where Ue (x) = x+1

    show that v satisfies
    \partial v / \partial t = 2 ( \partial ^2 v / \partial x ^2)
    when
    0<x<1
    t>0

    show boundary conditions on v(x,t) are  v(o,t)=v(1,t)=0, t>0

    find the relevant intial condition v(x,0) in terms of f(x)

    when
    \partial u / \partial t = 2 ( \partial ^2 u / \partial x ^2)
    boundary conditions u(0,t)=1  u(1,t)=2 , t>0
    intial condition u(x,0) = f (x) for some function of f
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  2. #2
    Junior Member
    Joined
    Dec 2009
    Posts
    31
    Quote Originally Posted by harveyo View Post
    Define v(x,t) = u(x,t) - Ue (x)
    where Ue (x) = x+1

    show that v satisfies
    \partial v / \partial t = 2 ( \partial ^2 v / \partial x ^2)
    when
    0<x<1
    t>0

    show boundary conditions on v(x,t) are  v(o,t)=v(1,t)=0, t>0

    find the relevant intial condition v(x,0) in terms of f(x)

    when
    \partial u / \partial t = 2 ( \partial ^2 u / \partial x ^2)
    boundary conditions u(0,t)=1  u(1,t)=2 , t>0
    intial condition u(x,0) = f (x) for some function of f

    i was starting out with
     <br /> <br />
2 ( \partial ^2 u / \partial x ^2) = x+1<br />

    I just cannot get my head around this question
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