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Tried to find in textbook but failed. I really need the analytical solution to the following PDE (diffusion from the infinite length cylinder, two-dimensional crosssection):

$\partial_t C(r,t)=D\frac{1}{r}\partial_{r}(r\partial_r C(r,t))$ with the following boundary conditions: $C(R,t)=C_0$ - the concentration of the cylinder is kept constant, $C(r,0)=C_{init}$, where $r>R$. Initial concentration in the domain is constant as well.

Need the analytical solution in the domain $r \geq R$.

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I suggest you consider asking this question on math.stackexchange.com instead – Yemon Choi Nov 8 2011 at 19:56
Added to math.stackexchange.com as well. – Alex Nov 8 2011 at 22:04
Link to MSE question math.stackexchange.com/questions/80346/… – Yemon Choi May 11 2012 at 1:37
Obviously, this should have been closed months ago. – S. Carnahan May 25 2012 at 9:18

## closed as no longer relevant by S. Carnahan♦May 25 2012 at 9:17

I've got it answered on SolversMarket. The procedure was to introduce variable transformation $\ln\frac{r}{R}$ and then just do the same stuff as to derive the boundary layer as in the case of planar interfaces.