NDSolve::bcedge: Boundary condition c[t,5]==Cout is not specified on a single edge of the boundary of the computational domain. >>
I'd like to plot $\frac{\partial}{\partial t}c=\frac{d}{r^2}\frac{\partial}{\partial r}(r^2 \frac{\partial}{\partial r}c) \equiv\Delta c $ with the initial condition $c(0,r)=c_{0}$ and the boundary conditions $\frac{\partial}{\partial r}c(t,0)=0$ and $c(t,R\in\mathbb{R})=c_{out}$ where $R$ is the radius of a circle. I know the analytical solution and I know how the profile looks. I'd like to use/learn Mathematica because it often helps if you can make a quick plot of unknown shapes.
NDSolve[{D[c[t, r], t] == d/(r^2) D[((r^2) D[c[t, r], r]), r],
Derivative[0, 1][c][t, 0] == 0, c[t, 5] == cout,c[0, r] == c0},
c, {t, 0, 10}, {r, -5, 5}]