defining Heat Equation

**harveyo** · January 26th 2010, 04:01 PM

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 $f$

**harveyo** · January 26th 2010, 05:21 PM

Originally Posted by harveyo

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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