  We investigate the distribution of work performed on a Brownian particle in a
time-dependent asymmetric potential well. The potential has a harmonic
component with time-dependent force constant and a time-independent logarithmic
barrier at the origin. For arbitrary driving protocol, the problem of solving
the Fokker-Planck equation for the joint probability density of work and
particle position is reduced to the solution of the Riccati differential
equation. For a particular choice of the driving protocol, an exact solution of
the Riccati equation is presented. Asymptotic analysis of the resulting
expression yields the tail behavior of the work distribution for small and
large work values. In the limit of vanishing logarithmic barrier, the work
distribution for the breathing parabola model is obtained.
