1. ## 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
$t>0$

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 $f$

2. 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
$t>0$

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
$

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

I just cannot get my head around this question