  The study of the density evolution naturally arises in Mean Field Game theory
for the estimation of the density of the large population dynamics. In this
paper, we study the density evolution of McKean-Vlasov stochastic differential
equations in the presence of an absorbing boundary, where the solution to such
equations corresponds to the dynamics of partially killed large populations. By
using a fixed point theorem, we show that the density evolution is
characterized as the unique solution of an integro-differential Fokker-Planck
equation with Cauchy-Dirichlet data.
