Exact results on diffusion in a piecewise linear potential with a time   dependent sink
  The Smoluchowski equation with a time dependent sink term is solved exactly. In this method by knowing the probability distribution at the origin P(0,s), one may derive the probability distribution at all positions i.e., P(x,s). Further the exact solution for Smoluchowski equation are also provided in different cases where the sink term has linear, constant, inverse and exponential variation in time. 
Diwaker and Anirudhha Chakraborty
quant-ph