Interesting. Let's develop that a little:
u=u(x,t)
du/dt = A*(d^2u/dx^2)
u(x,0) = f(x)
u(0,t) = 0
u(L,t) = V
Let w(x,t) = u(x,t) - (V/L)*x
Now,
w(x,0) = u(x,t) - (V/L)*x = f(x)-[(V/L)*x]
We can just call this g(x) so that's fine
w(0,t) = u(0,t) - (V/L)*0 = 0-0 = 0
w(L,t) =...