Diffusion in a Disk with a Circular Inclusion

We consider diffusion in a disk, representing cell with circular interior compartment. Using bipolar coordinates, we perform exact calculations, not restricted by the size or location of intracellular find Green functions, hitting densities and mean times to move from compartment cellular surface vice versa. For molecules diffusivity $D$, are proportional $R^2/D$, where $R$ is radius cell. explicit expressions for dependence on $a^2$ (the fraction occupied compartment) displacement center distributions initial conditions that (i) uniform nuclear surface, (ii) (iii) given density particles diffusing surface.