I have the diffusion equation with initial conditions c(0,t)=c_0 and c(L,t)=0 where c_0 is a constant. Also c(x,0)=0 for all x0. How do I solve this? I tried fourier series, but end up with an equation which does't fulfill the criterion.

Question

I have the diffusion equation with initial conditions c(0,t)=c_0 and c(L,t)=0 where c_0 is a constant. Also c(x,0)=0 for all x>0. How do I solve this? I tried fourier series, but end up with an equation which does't fulfill the criterion.

jamesj · Answer

Well, whatever else, you know that in the steady state
c(x) = (1 - x/L) c_0

anonymous · Answer

yeah, I do. But sadly, steady state is not what I am looking for. I need an expression for the concentration at any given point at any given time. :-/