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Thread: defining Heat Equation

  1. #1
    Junior Member
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    Red face defining Heat Equation

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

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

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

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

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

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

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

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

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

    i was starting out with
    $\displaystyle

    2 ( \partial ^2 u / \partial x ^2) = x+1
    $

    I just cannot get my head around this question
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