# Definition(s) > [!NOTE] Definition () > Contents > [!Example] Example > Consider the temperature distribution in a rod of length $1,$ that was at equilibrium temperature of $0\degree$ and insulated on both ends. > > ![[Rod|300]] > > We assume the rod can be modelled by the line segment $\Omega=[0,1].$ Then the temperature distribution can be modelled by $\partial_{t}u(x,t)=\partial_{xx}u(x,t)$for $0<x<1,t>0.$ > > We know that the temperature inside the rod was initially $0,$ that as time $t=t_{0},$ so we impose the initial condition $u(x,t_{0})$ for all $0\leq x\leq 1.$ > > To ensure the behaviour of the solution $u$ at the boundary we impose a [[Neumann Boundary Condition|Neumann boundary-condition]] $\partial_{n}u(x,t)=0$ at $x=0$ and $x=1.$ # Properties(s) # Application(s) **More examples**: # Bibliography