I am trying to solve following differential equation using separation of variables
$$ \frac{\partial C}{\partial t} = \frac{1}{r} \frac{\partial}{\partial r} \left(r \frac{\partial C}{\partial r}\right) + \frac{\partial^2 C}{\partial z^2}- \frac{k}{D} C $$
Subject to initial condition and boundary conditions
$$C(r,z,0)=C_0 \\ \frac{\partial C}{\partial r}(0,z,t)=0 \\ C(R_0,z,t)=f(t) \\ \frac{\partial C}{\partial z}(r,0,t)=0 \\ C(r,L,t)=0$$
But I want to ask is this solvable with separation of variables? Is there a better method?