I have been struggling with this 2nd-order PDE. I need to solve it using Green's function:

Heat equation for conduction in a bar, with Neumann Boundary conditions:


Initial Conditions: U(0,x) = f(x)

Time, t>0


f(x) = x for 0<x<(L/3)
=0 for x>L/3

Boundary Conditions:

Ux (o , x) = 0
Ux (L , x)= 0

Any ideas? The equation seems pretty standard and straight-forward but the boundary conditions seem difficult to work with.