On the time-dependent diffusive interaction between stationary sinks

We present an analytical approach in order to investigate the time-dependent diffusive interaction between stationary uncharged sinks of different radii. It is found the general solution to the corresponding initial boundary value diffusion problem for the case of two ideal sinks. Using obtained exact solution we propose a new more accurate monopole approximation and compare it with previously known time-dependent approximations. The characteristic relaxation time for the transient rate of absorbtion is also calculated. In addition the exact long-time asymptotics for the absorbtion rate of diffusing particles into a sink is derived.