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The Smoluchowski equation with a time dependent delta function sink is solvedexactly for many special cases. In all other cases the problem can be reducedto an integral equation. It is shown that by knowing the probabilitydistribution at the position of sink, one can derive analytical expression forprobability distribution everywhere. Thus the problem is reduced from a PDE intwo variables to an integral equation of one. As far as the authors knowledge,we are the first one to provide an exact analytical solution of Smoluchowskiequation for a parabolic potential with time dependent sink.

Some exact results for the Smoluchowski equation for a parabolic potential with time dependent delta function sink