I am looking to solve the PDE that takes the form of $$\frac{\partial C}{\partial t}-Q(t)=D\nabla^2C$$
where $$\nabla^2C = \frac{1}{r^2}\frac{\partial}{\partial r}r^2\frac{\partial C}{\partial r}$$
I have read that eigenfunction expansion is an option for homogeneous boundary conditions. My boundary conditions are the following:
$$C(r=0,t) = A(t)$$ and $$\frac{\partial C}{\partial r}\Bigr|_{r=\bar{R}}=0$$
where $\bar{R}$ represents the distance from the source where the insulating "wall" exists.
My initial condition is:
$$C(r>0, t=0) = C_b = 0$$
Do any solutions exist for this problem statement?