The following pde is (approximately) the leading order homogenized form of the local mass transport equation with a non-linear metabolism (in symmetrical spherical co-ordinates):

\begin{equation*}
\frac{\partial c}{\partial t}+\frac{K}{r^2}\frac{\partial c}{\partial r}+\frac{Da~c}{c+n}=0
\end{equation*}

My question is, if this is applied over some 3D sphere (with an outer and an inner sphere) then what would be the appropriate boundary/initial conditions? A no flux BC on the inner sphere seems to imply that concentration should be zero throughout the domain. (K,Da,n are constants).