Model partial differential equation problem. Consider a infinite rod with the temperature at a specific time $u(x,t)$ if the initial temperature is constant in $(-2,2)$ and and zero outside.
I need the boundary and initial conditions for the above mentioned situation. 
I know for sure that the boundary condition outside the cross-section must be the limit $\displaystyle\lim_{|x|\to\infty} u(x,t)=0$.
Not sure about the inside,
is it 
$u(x,0) = A$ and $u(x,0) = B$ or $u(-2,0) = A$ and $u(2,0) = B$ (where $A$ and $B$ are constant).
Can someone please exchange their insight and say if I'm on the right trail?

You are given the boundary condition as you specify, and an initial condition as follows:
$$u(x,0) = \begin{cases} A & |x| \lt 2 \\ 0 & |x| \gt 2\end{cases}$$
That is sufficient to solve the equation and get a unique solution.
